miljan pavicevic - geometrija za viii razred osnovne skole
TRANSCRIPT
II0tErPil[lA vlllPASPtI 00n0BrE rixdrr
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0lttIPIl3A VIt PASPIA 0Clt0BHE lntlr E
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Peqeme{r!:np ha EaHAut, npoo.cop Oap{aqeyrc{or Oary,rera y EeoryaryEparuqa su-sotua, npoo€cop npBe BeMyEc*c rryuasrje, 3eMyclooprcole Ue.$uh, trpooecop, trorohnfr Epc(ropa ocnoBEe rnore
"nerap (oqrh" y 3eMyny
Mupo.b!6 Or utoaul,, rpoo.cop, I{pyue!1& BnlII
3A tunaId\i 4pa^oelnB il. Joko'ti, ypeagar Hukold i'4;aloxo1uh, rerh ype!8nnEopfu no,o0nt, !!p.ktop Mtpja\a noaosuh
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CA,I{P}I{AJI. Y3AJAMHIj ONHOC I]PABE T,I PABHI1
1. olpcb.Ho.r paBn!2. Y3rjarrr nonohaj npcBe I paB k3. IIpaBa mpanema ca paB!!4. IlaBa lopManHa Ea paBan
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It. oPTOfOHAJIHA (HOpt\tAJl HA)IIpOJEi{UI,tJA TArlXB, ny)t(,l U up BE HA pABAH
L Opro,utsrnH! trpoJekurja .rqh,2. Oprororarna npojeqrja ayr{t3. OptoronorHa qpojetsqrja npaBe .
III 'IPOJEI{TOBAbE
HA ABE PABHI,I
I Ilpojedrrja ruq(e2. npojedrlja ayKr
IV. IIPOJEKU],JJA KBAAPA U KOUKE
l. ahojeKrtrja (Banpa
2- Rpoje(qrja koq(e
v. (ocA c,]I4xA
VI. [P!13MA
l. I]orrerap. Bpcre llo,rrerya?. Iipr3uc. apcrL tr ocoorxe rpaeMe
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4. Uprabe npmue ,
5. Mpexa r noBp0r'ra npi3xe6. 3anpeMla !p!3Me7. 3anpeMrra rpocrpare np'sse8. 3anpeuuaa Bruecrpare npmue
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Oco6rHe npaBr.rnne rrpaxrne
no3pE,ua {paMure
5. 3anp€Mnra mpaMdAr
VIII, EJIT,INCA
IX. BAJbAK
x. I{vt la
Mpixx r troBperna BoJbra
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Mpex(a r trougrrrH! (yre
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3. 3ary€nnsr .rome
XIl. GIIO)I{EHA TE,'IA I{3 flPAXCE
l. npoorn rera, fiorr{pabc r Atxer$rottparbe
xtll 3AnAUn 3A nOHABJ'bAI5E
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He iexe Ha xcroj npaBoj no(yuajre 4a npoveHxre nonolkaj xaProHa'
a aa npn ToM He Methare norloxai onoBaHa' yoqaBaMo na y roM. cnyqalyKaiToE y upocmpy Moll(e 3zly3llMarll caMo jeaalr nonoxaj. Axo caaa
"ilr",r i.rpioo", i" rpxorrl oa6tana sayenuajy ucru nono)Kaj, Bl{aeheMo
Ia u cBar(r rapTolr arMa ucTlt notoxal, na 3a byqyjeMo:
. PaBatr je oapebetra tprMa raqt{aMa |{oje lle flpnnaaaiy ncroj flpaBoj'
143 oBor cnealt !a je paBalr oapebesa:
1. [IpaBoM I Taq(oM Batr Te IIPaBe'
2. .{reua nPaaaua (oie ce ce(Y,
3. ABeMa trapa,lerEnM flPaBaM{'
CBaKn oA oBa rpx crycaja cBoal ce Ea oapeteEocr paBHit ca rpltraqKe, KOie He Jlexe Ha LrcToj [pa3oj'
Ha nohMeot ,[Lara je npaBa p H Taqxa C BaH rhe fcn 4) y3MHMo
", ";;;"i;;+ npourBorbge raqxb A I E Taq*e A B, C ne 'texe;; ;i;;;r;j, n'a xpoe *ax MoxeMo .ocraBxl'r j'rHv ca'o jerH)
'paBaH. Ha crxqaH llaqrH o6jaclltt x [pyra
'Ba cnyqaJa
2. Y3AJAIIIflI{ IO,'IOXAJ NPABE I'I PABHI'I
Axo ie npaea olpeheHa raqKavd .,i4 x N ftoje nprnaaajy paBrx d(ca. 7t. onna cu" raqr<i npaa. p npltflamj] paBhn d, na (axeMo: 0plBa
i.x" y paeon axo ca EoM rrua 3ajeltrFqxe ]lBe raqxe'
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Cr. 3
a
Cn. 5
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Ar{o npaBa / l,l paBaH a ,Majy cavo jeaHy 3ajeaHuqxv ra,rr(v p(ct- 7) KallreMor npasa I npotrrle paBaH o. y iaqxu p, rojy gosilroraqxa npoaopa.
AKo npaBa q I paBaH a HeMajy rajertlltgxrx raqaKa, oHna jc npaBa qnaparenEa ca paBHt!.
3. IIPABA IIAPA,IETHA CA PABHII
Vauarc laa pa3rr.rqr.rra i(aproHa o6Jnl{a npaBoyraoHrka, IIa jeAny{TpaHEqy Marber -flpaBoyaaoHrrra nocraBrire Aa nexu y BeheM npaBo_yraoH{ny (cr. 8). MerLajre noroxaj MaBer npanoyraoxnia ABCD
_raKo
na v) ctpaHrua 48.flexu y paBH Behet raprorri. Axo npaBa orpeheHa{TpaH}uov AB ncxr y paBHH, Ka(aB je yJajarrH no,roxal noaee oaoe.heHe .rpaHxuoM CD npeMa roj paBHM? iauro?
3ax.nyuyjeuo:
. Axo je npaBa Batr paBnx naparertra ca {er{oM rrpaBoM Te paBEx, oHaJe lrapanenfia n ca ToM paBf,r.
4. IIPABA HOP,IIAIHA HA PABAH
Ha aacry xapruje, kojfi npeEcraB]rr,aI'oIleJI paBnfi, nocTaBu?e koqxy, u y Te-Metry A noByquTe Hel(ornko IlltaBfix.OaMax youarauo 4a rJpaBa oapebeHa 6oq-rloM lrBnqoM AE npoanpe paBan y raqKx A;-raxolje yoqaBaMo Aa je oEa EopManEa EaflpaBe 4 r c (cn. 9). 3arnro?
flpaBoyrrfi Tpoyrao noAecE raKo !aMy ce TeMe npaBor yrJra noKfiana ca Taq-I(oM A, a jeaqa rarera ca 6oqnou uguqouAE. Axo fipaBoyr"IIr rpoyrao o(peheMo cn. I
a
Tar(o aa ce (areTa [oltJtorrbeHa ca 6osnoM I'lBI'rqoM A-8 Ee rIOMepa, apyraxarera he 3av3lrMartr pa3Jltrqure nonoxaje' flpaae oapelene noJrox{ajeM
6osnoM LrBLrqoM A-B Ee floMepa, aP
xaTeTa he 3ay3DMaTd pa3'!qqDTeapYfe r(aTeTe cy HopManHe Ita npaBy3a rro? l'13 oBor nPolBna3tr:i
IIpaBa je EopMantra Ba cB{M,npaBItMa jeaH€ paErtr l{oje npotra3e l{poo
afio je sopMarEa 6ap ua aae o,q lbnt. 3a lakBy npaByf,reE npoAopr aRo le EopManrra oaP Ea a6c*"*a*b li ja nopua.nna nit paBari a ra'rka A je lpoaop [opuane'
I43 lare raqKe P saH paBHx p l\roxeMo noByhl 6e]6poi npaB \ soje
he nponlrparfi paBan. floxaxltMo na je cavo jeaHa npaBa d HopvaiHa ua
Ty paBaH.
orpebeEy 6oqHoM IrBItqoM roqKe.
OBaj ornea hei,Io x3Bplnllrn noMohy aBa npaBoyrJla rpoy.na. JeaaH npa_
BovfJtl,t TDoVlao MoxeMo nocraB TH Taxo 1a M) 'e leve npaBor ytrla Ha-
,uin y riui" npnropa 6x,1o j{nje npaBe roByqeHe H3 ra'rfie P npr 'leMyienHa KaTera npr{ \ naroj paBH . a apvry Kaler} yBcK Moxevo nok-,onrr, au !"ao" np;Bov (d,D xrr , c,l 10). AKo nocraBlvo jour jcaag
npaBoyfru Tpoyrao, TaI(o !a My ce TeMe npaBor yrra Hara3n y Tarrklt
nboaoi,a, a jeaia ftarera !a ielrrl y paBHr. B'rtreheMona 'e npyra ,{arcraolli 'io*ronrt,
.a narrM npaBarva (cn. l0t ocrv y jennou c,lvTajy (npaBa a.
cn. 10) xa! (axeMo aa je npaBa HopManEa Ha paBan. Ha oclroBy rora3a,{Jb) qyjeMo 4a ce Hpo3 Aar) raqEy ) npo'Topy Ha ralv paBaH MoxenoBvh,r caMo leAHa noPMara
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HajMarle la'raxa oapebena paBan? Kojn jotu ycroBi.rcDy16eH?
npas x oapebeHa jealla paBaH? Kojh jou yc,loB
BE)l{EAtt A
I. Ca xonlrlo jeMOpa aa 6yae
2. Ca xonlrKo jeMOpa aa 6yae
5
3. Kaxaa ysajavrr fonoxaj Mory nMarrn npaBa u paBaH?
{ Xarar ysajauuN nonoxai Mory rrMarn rBe npase:a) y paBEr,
E y rpocropy.
5. V npocropy cy lare 4 raqxe A, B, C v D, *oje ne npunaAajyEcroj paBH[ on 6oj]\ no rpH He nprnaAajy rcroj npaBoj.KonLiKo ce paBEn Moxe (po3 Inlrx fiocraB'rrli?
6. I{onrko je paBnr orpebero.ca rpx -npaBe
Koje ce ce(y y jeatojTaqr(E, a He flpunaAajy ncroj paBHu?
7. 3arqt je ocr'ronaq rponoxaqa nocrojan? I,Iueuyj jolu Hexir npea-MeT Ca ?p, ,,HOre"
8. I{o:ruxo je paBlr oapebeHo ca 4 6oqEe rBlqe KBaapa?
9- I{o.rrxo ce HopMajrHxx rrpaBnx Moxe IIoEyh,l Ha paBaH rr3 jeAEeTaqke BaH Te paBH,l?
10. Kaxaa je vehyco6Hr nonoHaj npaex., xoje cy HopMarHe na tcrypaBaR?
ll. Konlll(o .ie paBH[ oApebeHo ca 4 fpaBe koje ce cexy y jeAnojTaqr(x, a oa (ojrx IIo rpr.r Ee flprrraaajy rcroj paBEn?
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il
AI,IEAAP
Af,eaap je reoMerprjcRa ourypa xojy o6pa3yjy aBe fonypaBnn ca3ajearq.r*oM rpatrrqEoM [paBoM,
Ha nplMep: AI{orao lrrro je [o(a3aHo
jeaaH Kapros ofuruKa fipaBoyraoslKa npecaBlrjeMoHa c,lrqu 11, ro6nnn cMo reoMerplrjc(y ourypy_ koja [peacraBJba rneaap. CBaxu aeo l{ap_
TOHA npeAC',raBJBa nO lenHy nonypaBaFaola ce 3oBe cTpaHa axeapa, a 3aJelH ckarrpaBa - nBnqa al{ellpa,
CTpafle anelpa ,qene npocrop a aBeo6nacrx Koje 3oBeMo: ytlyrpalrrrba Ir cflo-JbarxBa o6nacT alteapa,
Ha crrqu 11 npuKa3aE je aneaaPca rrBuqoM m n cfpaHaMa alr p (oju slr_raMo a{eaap cmF fint alreaap dABp'
Ha llBlrqu AneApa (CD, cr. 13) yosff npou3Borblry raq](y ,I(. I43 raqxeK y pasH, (! noaxrHH HopMany KA Ha rBxuy CD rj. KAICD. I nop-ManJ (8 y paBHx B rj. AB L CD. Te aBe xopMare KA n KB oapehyJypaBaE flopMaiHy Ha xBUuy A[enpa { y rbuj qtse yrao arcApa AKBxoju ce 3oBe Harfi6nu yrao lreApa. yoqn caa Ha rBllrtlr CD HeHy apyryTasKy K n fi3 II,e Ha cBaEoi ctpaBn alreapa noByqn EopMane Ha tBnqyrj. K,A,I CD a K.B.LCD.
Ci. 12
= crPava
. "4g
Cr. 11
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^- Oni rop,raale onpeh)jy .raKohe paBalr HopMardy Ha IBr Iy arrenpa.iL[c oDe paBEn HopMaJrHe Ha l'BHuy nfieApa cy vehyco6Ho n]pa,re,rue,Ptcmjace fi3ueh5 $ux je KKi. Tpanc,naiopnriu nor"paner jean" oaEXX rao,fy ce paBnn AoBecTlI Io noxralar6a, u raaa he ce kpaqr yrnoBaretyco6Eo nonnairarr rj. yrao A1(B jeaHaK je yrry A,(,Bi.
3Eaqu Aa:l. BerHcsHa Harll6Hor J rra 3aBrcfi oa floroNaja tberoBor reMeHa Ha
I]lBnq lneapa.2. PaBaH oapcheHa xpauxMa Haru6Hor vrra Hovl\ra,tHa le Ha Bruy
affenpa,3aruTo?3. CBa(a paBag, rropMaJrna Ha uBurly arleapaj ceqe beroBe crparie
y nBa flpeceAa Kojx o6pa3yi) Har'l6HH lrao alletoa.
Cx l5
Ben[quHa Auerpa oapebyje ce BerxqusoM rraru6Eor yrna.Anelpr cy jeAHakr ar(o cy nM nara6Hr yrnoBr.r jeAfiaxfi.
Alreaap je npaB axo je Haru6Eu yrao npaB cri. 12. llpeMa roMe aa,r4 je HarI,l68Il yrao olrrap uJr,l ryn Anelap je ornTap lt,rl{ ry[. AKotrpau Harfi6fior yrna npxnaDajy ucToj npaBoJ. oHaa cTpaHe aurrlpa rrp14-traaajy jeAnoj paBnn, a raj ane,4ap je onpyx{eH (cr. 14).
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POfAJb
Pora*, je reoMerptrjcxa $nrypa xojy o6pa3yjy rptr {ttr B{Ile trorry-trpaB{x r(oje ne nexe y l{cToj paBEn, a trora3e Il3 ncTe Taql(e n Ilpoec;a[e,ase cyce4se norylpaBe nocraB]bena je psBau.
nocMarpajMo crlrl(y 16, 3ajeaElrqKr{ I1oqeral( rxx nonyrpaBnx 3oBe
ce Bpx por;a (S), no,rynpaBe cy IrBnIle por?'6a (SA, SB, SC, .. ), n<>
lBe y3acronEe nBi{ue oapetyjy uBnqHII yrao, r'rn crpaEy por?'ha.(lAsB, IBSC.,.).
CrpaHe por.t a o6pa3yjy3ajeaso noBpupor,'u. lio ree ) ,aIrbnnc crpane o6pa:)jy.qneaap por?6a. PoraJE, ca rpn crpaHe 3oBece Tpocrparifi porars, Itn[ Tp{eaap, ca qe_
Trrpx cTpaHe - qerBopocTpaH[ poraJb IITI-
Cr. 16 Ci.17
AKo por aJr' rrpecec.vo jPlnov paEBU xoja ceqe cBe rleloae BBkueu axo 1 nire"ery i(,6rjevo rcnynveu Hill KoHBexcan vHoroyrao (c,IKal9c), onaa je puraLb cflynq.H ,lrta koHBPKcaB a axo le npeceK yayo'rbeii-Mlroroyiao,6naa je poia.'l yay6.r,en tnr (oH(aBaIr (crlixa 196).
V na,'leu re,raramy y'ruMahcvo y o63xp caMo ncnynqeRe por'beBe.
flncrasDMo MoIpJI por?'ba vc xojoM EeroBoM crpaHoM Ha paBaH. Pa1B,r-
iarbeM rhercBe noBprrrrr y rJ paBaH, TaKo aa cBe IneroBe uBxqe I,l crpaHenp[naaajy ,croj paBEI-i, Ao6xja ce Mpefia porJ6a.
ii
iarbeM bercBe noBplrrlr Y T
Mpexy por,'La MoxeMo LoEcrpyucal! (ar Eaqpra-Mojelax .io ipyror.ca 3ajeantqrlM ieMeHoM S (cn. 18)
cyceaHa [MaJy 3aleafil'rlxn Kpa(.
nBuqfie yr,loBeTako aa flo aBa
I
Ib roEcrpyrqde Mpexe Buan ce .qa je Moryhe Moaer porrra Harpa-
- iciro axo je e6rp uiaqlrux yrnona Mabn oq 3600.
Ci l8
Ha ocsoBy rora 3akrbyqyjeMo:36ap cBux IBtqIr[r yrnoBa ]rcayflqenor por6a MaItIlHa renxMa roja cy orpaHfiqena paBHsM noBplnltMa
-*r2l, [rpaMulla) nojaBjbyjy ce poribeBlr, na ce ral(Ba
iltt!:&acrrM.
je oA 360'(Kao Korlka,Tena 3oBy
Cr. l9
iAE)(EAtITA1. Hanpaar i,roaen rpocrpaEor por'6a axo cy I'tBIrqEIt yrJloBxl
a:60', b:45, u c:75'.2. Hanparr Moaen arreapa oa:
a) 60" b) 90'.
3. Hanparu Moae, aBe paBElI xoje ce ce(y noa yrnoM oA 600.
4. HanpaBr MoAefi qerBopocrpaEor porJba qtj{ cy yrroBa no 60c.
I. OPIO|OHA,'IHA (HOPMAJIHA) npoJEKUlrJA TAqKE-Ayxd H npABE {e pleAH*"-" ""''"'
__.. .lla.6acvo reoMerprjcBa rera npc/lcraB,,r,aJtr, (Irt(oM y paBHL no-TpeoHo le 4a sHaMo ageecxa noasrrrj,i*o a"-.0 ;, ";;;;, ;;;h; ;;".;11'",J"J,T1 ,I,tX.X"f,i ^l1T
,$!1,,?;oaHoct{ r.{3MelJ.\ o,qroBapajyhHx ereMeHata Ha rejv
I. OPTOTOHAJIHA (HOP]I,IAJ,IHA) IIPOJEXUI,JA TAqXE
I4J raqxe A {cn.20) cn]UreHa je HopMana Ha paBafl p. Ilo4HoHjcHopMare A, 3oBe ce opror'daalria (aopuarra) ipojexqnja,rarx" i " ,i",ir'ir.PatsiH p :oje ce trpojexr'a pr"i" i,r, pai,"i ipoi",i"a,i.
-i1i'"jr""o]{l ;;opojekrJjyha rpaBa raqxe A. Vra.ruenocr .raqixi A ri e,rb""
".'*oi"Taqke A y o4Focy Ba paBaH p.
9.4 (+3 )
ct 20 cn- 2l
___, C o63tpoM Ha ro aa ce raqxa voxe Halla.lirl,l ca pa3Hkx crpaHa,trpoler(Tae paBUH, To ce.rcopelr xore craa?Ea op.ar"a* +,.rr,o 1" i6,rniu3naA paBHI npojekqnje, a nDell3Hainpojekuuie. a*o'c" rri*, ;;|.i";''i - a(o Je raql(a lrcno! paBdrr
Jeasaxa ca caojou npojexqrjoM , *d"r'o*:'rT j:o'o.o'aHd' oHla Je raqxa
llo.Marpal c,rrrKv 21. Kora raqre A je {rJ). a xma raqxe B je(-2), xora ra'rke C je 0.
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2. OPTOIOHAJ'IMA (HOPMA']HA) NPOJEI{IIIIJA NY}I.U
flpojeBqujy ayx{n AB fia paBa ao6njaMo Kaa cBar(y raqr{y Ayxa-aB trpoje(ryjeMo Ha npojeKrHy paBaH, CKyn rIIx npojenurja npunararlze Koja cnaja lpojeFqEje [pajIbLD( TaqaKa rc nyxtr- 3Haslr,.!a 6ucMo.olpeaunlr npojekrlujy !yxu, norpe6Eo je aa npojekryjeMo (pajlr,e raqlrere Ayxn (cn. 2D. ny)x A'B' je oproroaarEa rpojekqltja nyxtt AB yFsdtr d. PaBaH xojoj rpura{ajy ry:'{]j AB \1 A'B' je npoje(ryjyha,.paBaE lryxr.r AB, (oja je {op arrlla rla npojexHy paBali p. yoqaBaMo aafu AA'B'B rrpaeoyrru rpane3 jep je AA'l]Bts.
Axo caaa raj rpane3 o6opuMo oro npoiexqtje A'B' y paBHu p,-
.ro6EheMo ra y E,eroBoj DpaBoj Bennq'lHn.
Ci.22
y3Mure (apron, EaqprajTe lra IneMy lty)r{ AB cr' 22 'l rocraBl'Ifltra HopMaJrso Ea paBaH p. Cnycrrrc cala fiopMare u3 A Ir B Ha paBaEu cnojrr. Taqr(e A'B'. O6op rc HaproH or(o a1*'u A'B'fl.{ He nanHe \paBaB p. y o6oppHo\,t rpane3) hpa( AoBo le npdBa B,,lllq Ha !\x qB
v rrpocTopY.
5 B'
Cn' 23
AI{o caaa ayx AoBo r'r neny Kpojekqrjy A'B'npoayxlMo olr€ hecc cehH y ir.Koj raqKH S. yrao roju re opaee 3afinanai) roee cc uarl|6suyrao nJ r{n lpeva paBHx npojexuuje. Taj yrao Moxpvo oape[rr x aKC!
x3 Ta,rKc Ao noB] 'rcvu napaje,r) ca A'B' (cn. 2:\).
3v 56'
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_IIpeMa roMe koncrpyKqrja npaBe Be,r{rrrHe Ayx,l n oapebfiBar6euaru6Hor yrna Moxp ce rarro ltJaecr,r, axo ru ji no:xara ie,rrrlnairpojeKqnje Ayxrl u kore lneriltx kpajeBa cr.22,
Haqprajre Ayn{ AB napa,re,rEy ca paBEr p Ir Habrrc r6€Hy opro-rofiarHy npojeftuujy AB'. [Ira MoxeMo pefi{ 3a Ber'ruqrHe AB;A8?3arxro? Kor KU je Har r6HI yrao nJ )l{l, napa,lc,lHe ca npojehuu-aKnv paBHr? A4ebajrc HarH6H jrao avirr AB ripeMa pacH[ p (cn.2q).nocMarpajTe rxra 6uBJ ca npoj(KuxjaMa nlxx AB axort,cH Har 6un vraopac?e. (y AaJbeM u3naraby noA HaguBoM npoje(Urja troApa3yMeB; c€oprofoHarrEa flpoie$quia.)
CL 24 Cr. 25
3a,qarax 1. OproroFaina rpojekqfja ayx([AB Ea paBrrLt x3Eoc[ 3cm,$ora AA'-2cfi r.r R.)ra BB -6cm. Olperhrrr noJroxaj re ayxr| upre-n oM,- r{oricTpyncaTfi u r$paqyEaT[ 6eHy rrpaBy BenxqrrHy r olpeallTurlaruoEu yrao.
Ilocvarpaj c,luKy 25. Ha cnrur je A,B, 3cm. AA'IAB u BB'LIAA'. a AC A'B'. yruo a je Haru6Hfi yrao ,yxl.r AB npeMa prBBx.AABC je npaBoyrrr. Karera BC:BB' CB':6 cnd-2im:4 cm.
AB,:BCt+AC2
AB':4!+32
AB'::16+9
AB:11'F
AB:5cm.
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3. OPTOTOHAJIHA IIPOJEI(UI'JA IIPABE
l{eo E l{on fipojekquje ly)l{lrJ noa fipojekql'IjoM rlpaBe Ha paBaE no_
{q eBalro cxyri ripojexqujd cBnx raqaKa npaB€ Ha ryraBau. Aa 6ucM@
EEu trpojexqujy npaBe Ha paBalt, aoBorbEo je aa BateMo npoje(qsjyeiy 6eEri1 raqaxa. 3allrro?
Ha cruqlr 26 rpaBa A'B' jeqniexqEia rrpaBe AB na paean p.lirlo je npaBa . AB naparlerlra ca
FBE! p, OHDa le Orra fiapaJreJlHa Ilta cmjoM npojeku[joM A'B'. 3aurro?
Cr.
B
Ct. 26
Ha c.I:,tt\i 21 DpaBa CD' jeOmrap yrao l{oju npaBa CD 'rlrHx3oBe ce Harx6gn yrao npaBe npeMa
EE}l{BAIbA
npojeKurja npaBe CD Ea paBEE_'p-.ca cnojou npojerqltjoM CD'Ea paBaErpaBHIl.
,?
l. lllra je
2. Kaa je
3. (aa jc
oproroHanHa npojeKquja lyxu Ha paBas?
oprolodanlra npojexqt ja ryxn jenHaxa caMoj Ayxli?
oprorolrarlHa llpoje(quja ayxu raqxa?
4. Axo jr nyN AB 6cm, a rhcHa npojeKurja Ha paBaH ^'B'
3cm'x,,,'rxl jc narr6nH yrao re a)xu npeMa npojF'(rfioJ paBHxr
5. fls'ojeg4aj6 a\xfi 48 Ha paBaH je A'B' 8, I{ore !beHrr KpajrLrxraraxa c1 AA - 2. a BB' 4. oflpeall Harr6H yrao re ,r)xrtnpeMa npojeKTHoj paBHn qprexoM u lBpaqyEal I6eHy BeJIBq[Iry.
(ynyrcrBo: rpajme ra,rre oBe ayxlr Bana3e ce ca pa3trnx crpaBaopojexurixe paenl. rj. a1x npo! pe paBaH ly'r_ raqxr Ao noByuuvonaDaJerv ca A B',ao npecexa ca flponlxeIHoM /Jou: AOb&laMO TaqHy L.'fJricuarpal rpolrro AoB"C" h fi3pa'ryfiaj npaBy BeJlfi'r}tHy a)x Aetso.
cr. 28.)
14
6'Llnryiit-" "p"i"
\\uly KL' qa cn{rr{ 29. EpojeBn qa cniqg3Eaqe qefirpEletpe.
7, Aa,ra-- je^ ntojexux ja llNt na paBan lr (ore rseatx t<pajultxTaqaka. UApeIx aaru6nn yrao ri lyxn toncrpyxqljor, _ri
lgpa_qynal BeEy npaoy aeanrriy.
B.
Cr. 29
a) A'B':46) C'D':6B) gF:or) e'H':8a\ K'L'-Bb) Rs':8e),4.1,N,:12
AAI:2cc: _3
EE: 5
KK: 2
RR_ 3
trt,:0
BBt:5DD':5
HHI-OLL': -4ss':-12
Cr. 2E
IIL TPOJEKTOBA}bE HA ABE PABHI4
3e qrmrona.rno npojeKToBarbe fla aBe paBEn, [orpe6He cy xopr.r3oE-E (r,) a BeprrKarHa (Jrr) npoje(r[a paBan Koje ce ceky nol npaBuM!.p r .rEe reoMerprjcKj rfrrlpy, no:nar1 no4 rMe oM npaB Au.Aap.k i.npecex oBxx piBgr npaBa .r. HoJa ee roae oca_ npoiexuNjeE I.IE-
1. IIPOJEI{UI4JA TAqXE
Y3rE aBa (aproHa y o6nllky ABa noay-.lpsa EpaBoyraoHrrrr{a !l nocraBlr ux xao HacllIIIE 30a. Oprorona,rua npojerqdja raqKe A,EF ne npltnaaa ruM paBHrIM y xop!3od?aJ-ri trpoienrHoj paBnu (n,) je o3HaqeHa ca A'l nBe ce xopll3oEra,lrta flpojel{quja raqke A,r r- B€prulrarroj npojexruoj paBux (nJ ca A"Qn- mBeMo Beprrrkarfia npojekqrja raq(e A
Ka4 ce xop{3oHTa"1H" npoj.*rn" pn"u;dopE 3a 90', l<ao Ha cn. 30, r loeeae y ucryFB:rtr Ca BepTnKaJrHOM TTpOJeKTHOM paBHUt ItO-lrrJi ce nBe npole(qrle laql(e y le,qHoj paBHn.Ilr c:f,ue 30b Bunrlcc aa c) aBc npojpxu j(A' E .4", 3aficra npojeKrruje jeaHe .ra,{ke ytrpoc-Topy al(o ce Hara3e Ha npaBol r(oja je Hop-rarra Ha ocy npojekqaje.
2. IIPOJEI(UIIJA AY)I(I{
- Kao { Koa npojri{roBarba a}}{ Ha jp[Hy pasaH x oproroHanHa npo-letqtja Hr aBe paB8n aobxla ce xaa cc npoleKTyjy r(paJr6e TaqKe ayx[.Io6tjese upojexunje rpajrbr.rx raqara ayxn orparrqaBajy ayt(lr kojenpeAcraBJlraly xoplr3oHTaJlny It BepTIIKanEy npolekqlijy !yxu._ HaqprahcMo Fajnpe trpojeKurje Aylr(l,j Koja je napare.nxa ca npo-,eKmuM paBH Ma (cnr(a 3l), I43 crxKe ce B !n na cy oprorofiarHe4)ojexqaje oBe 4yx{q napareiH. ca ocoM npojexqfije H jenHafie ca nyx,y [pocropy.
b)
6fu
?
titi
t
Axo je ,qyxr napajenHa caMo ca ieAHor, ,pojexrHoM oaBEu u 3aKran,u-3B-ecrad yrao (Haru6nr_yrao) flpeMa trp]Toj irpojexruoj paenl, rala he,e!Ha rheHa npojeKu[ja 6nrfl napa.[erHa ca oioM npojei!rje u Kpaha,
l6
Axo ce avx naaasu v6eHa Dpojekunj; ce noxaanjiexqtje.
jelHoj npojekrnoj paBnfi (cntxa 32), jelHaca aaroM ryr(u, a Apyra je ua Ba ocn rpo-
tfzc" D'
B"c, D,
A' B' ft.
C& 32
li
R
a ,upyra he crajaru koco [peMa ocj]r lpojexqkje Lr Eo aenPFlniv 6ut''lellHaka !yxxi rbcH-_yrao npeMa ocl,l npojekuxjc 6nhe jelHak Hatu6Houyrry flpeMa paBflH. Ha cJIlull 33 nprka3aEa je ayx napaacana ca roDu_3ouTanfloM Ipole(rHoM paBHrrt,l Doa yrroM a noeMa ieornranHoi xoo_leftraoj paBH r. (A'8,--AB, A,,8,'<ABi.)
. ,4yx y npor:aoLrno{ nonoxajy sarEyra npeMa o6e npojexrHe pasfitlnpojeKryle ce K8o rxTo no(a3yje cr{Ka 34. h3 infixe ce itat aa iv o6et6efla npojeKqHle Kpahe oA !yxx. VonUlte nDs oOrOrOsaJrHOM {HooMirHor,rnpojekroBaby) na Her(y paBaH npojerusja riy*ri je najsr.rure-jeinaxa caAyxh xa! ayx crojn y cneu jarnoM no,noNajy y onHocy Ha npojefirHy11,"-:-l
(!l* napaierra cil. pasxs u ayx nproaaa parinal, y iaaxoirtrpyroM cnyqaJy oRa ,e Kpaha.
.'i t' z' C' D
A' B' tr.
i^.1
n,A' B'
Ci- il I
tTgsbD-!kFFFi,
iIIiIt.
Fr................
lII
iI
Ii
i
I
III
I
IlI
it!
II
iI
IIiI
I
l7
-F - xoq trpojeliroBarha reoverprijcxlx re,la jaBJbajy c,ryqajesu
-rrl BBxoBe IBuue Hricy na upreNl y npasol ae,rruurir, nbroi6uoqFrtr ra(o ce rr npojexqrje oaoehvie noaBa BerrxqlH, ;r*"qFttr_ ra(o cc rj apoje(urje otpebyje npaBa oe,rluaua ,,tyxt'.E @iacEaTU Ha cjeleheM npffMepi:
Cr 3t
HaupraJ npojeku,rje ny' i AB uA(1, 3), at4, 2t, a A,B.-gcn. (6pojeBr
2 reorcrpnlr 3! vttl psDer
r6eny npaBy eeatvuny, aro iey 3arpaltl lopea o3r]aKe faqKe
A,; ,8"
la
B"?---'
iiJ(
18
o3HaqaBajy yAarbeEocr ?aq(e. lpojeKrlr.rje, n ro npB{ 6poj yla,'beqocr oABepllrxamre llpoleKlEe paBsIlj a apyra yaaJrreFocT Taqxe oa xopn3oHTaJgenpoieKrHe paBHU.)
Ha oc,l npojexqirje npexeclr.ayx A,B,:3cm, I(pos raq(e A, tr B.noByqn HopMane Ea ocy trpolekqule, x y xopr3orrranHol flpoJe(TEol paBEuHa HopMany npeHecr ArA'-lcm, a y BeprlxanHoj A,A'- 3cm, ra(oxcro n BrB -4c@ u B,B' 2cm. Ayxx A'B' At'g" cy npojeKunje
1
i
Cn. 35
ayxtr AB. Npo3 raqre A' tr A" noByqr EopMarre Ea paBEr; npeceKoMlo6rjaru raq(y A, lpecetori HopMana xoje npona3e Kpo3 B'u B" ro6u-jerr ra.!(y B (cru(a 35). 3arru croj raq(e A fi B. At<o rya $ AA'B'BooopnMo o&o A'B' y paBa'l ,r1 ao6EheMo [paBy Benrqmy ayxx AB(Bznn crpaEy ll,cn.22). Iyrx AB je npasa BeJr'tqxEa Aare ryxq.
i\ + >8"
iBlx,..El-
no6[-
AB
a
IV. IPOJEKIII4JA KBAIPA 14 KOUKE
L ITPOJEI{UI'JA KBAAPA
llpoleurje rraapa uhre pasqE DpojeKryjyEpEf, Orpan[qetre xBu-E fuJ.r{uMa), a sBnqeErEa.ra, To ce npolellro-ttE€ cmAn Ha npojellTo-E6e iaqaxa.
(oqke ao6ujajy ce Tar(o rrro ce Ha o6e [po-cBe noBprru (oje nx orpaHuqaBajy. Ka(o cy
Y3Mure xBanap u no-claBlll e Ia n3Haa xoptl3olt-ta.rEe trpoiemEe paBHr (n,)x ictrpea BepTr(anHe npo-leKrae paBru (rL) Kao EacfiqE 36.
Xoprsonranxa npo-Fq{ja rcaapa lo6rja celaxo uro ce cBal(o Hre-mm reMe rpojeKryje HaIOpH3OUTarEy npojer{rHypaBaE (rr), a BepruKarrHatrporetq4a Tar(o [rT0 cecBztxo, I6eroBo TeMe npo-l€ATyle Ha BepluxarrrHylpoiesrHy paBaH (rr).
Cnajan eu ysacror-EEX trpole&q8la aoolla cespaBoyraoHrri. Kol csa(orTeraeHa npaBoyraoHrir(a cy]-nncaHa rro aBa croBa, 3a-mrc? npojenluje y xopr-3oETa,rHoj npojekrHoj oaBHuA'B u B'C'cy auM6H3 jetrpa8oyraoHnHa ABCD, aspojeKurrja A" E, Dpea-ctaartLa Bl{cltlty KBanoaABCDEFGH.
DL
.1
H':
F'G,
CG'D,
A'E' B'F'
20
2. NPOJEKIIXJA ITOIIXE
Hexc je rouxa oocTaBrbeHa xao Ha cnfiufi 3?. f]pojekToBa]beu cBlfxT€MeHa ,(oqxe A06rijaMo kao npojeKufije kBaApare. ,[,yxlna crpaalUcxBanpaTi le fi llyxxHa xafiqe npoje(roBaHe koUxe.
Xopnaonra,rna npojefiqujatroI1tre Je r(Balpal, iep cy aBeI6eBe CTpaHe napaJrenHe ca nl'na ce npoJer(Tyjy caoJoM npa-BOM BeJII,tqIHOM, OcTane CTpABexoq&e, lopMaJtHe Ha 11 ltpo-leKTyly ce y cTpaFDrIe r(Ba-apala.
Y orEocy Ea paBaE Jr2 Ta-(obe cy ABe cTpa e Dapatenleca t6our a cBe ocrate cy gop-ua]llHe na Je npolelrtoBarr,e rcToI(ao y xoprr3oETanHoj npojeftmojpaafil{.
C,. 37
l:: rr\s.-
/ ...1.. .,:..,.
',. .,/
,2 ,ffi;
"H:tt
V, I{OCA CJII4T{A
ClTIrra nexor reoMerpnjcEor re?'ra c?'ryxr'r fiaM tra floMohy H,e nobe-vo ao jacHe npclcraBe o reiry Koje oBa rpuEa3yje. HajBepHrijy cnukyTena np)xa Ha\,l {bororpao ja, jep ra np i(a3)je riqHo ral(o_ra HJuJeoko B nu. A,rH, oBaxBa clrrFa He 3aaoBo?'6aBc oHe yrnoBe koje HauJqpTex rpe6a aa r'rMa.
Kaxo ceax npetrlrer rn, rpx lxMoH3rje. a lprcx caMo nBe, To oHrpe6a na 6y!c Ha,,praH Tako aJ c) cBc rpl{ rhcroBP lllMeH3xjP B,lnrbMBe.
floclaB[Te t{uqJfi! MoaeJI I{o-rrl{e rcnpea Ber<or cBerJocBot lr3aopaTaKO !a jclHa cTpaHa (ouHe 6yde ncpa,renHa ca f,uaoM. a jenHa na HMa
xopr3oHrJ,rraF nono,Aaj. AKo,3pau cBerrocHor D3Bop.r na!ajy xoco Ha
paBan 3rraa, Ha 3ray ce nojaBr'Lyle ceE(a, Kola Mo)I{e aa IlMa Il o0rl,ll(trpnKa3aH na cnuqu 38.
G
Cr. 39
Moxevo yrerr na 3r,la npearraar'ba noijer{rHy paB€H, 3paun cBer--DCAOT r3BOpA, XOJn Cy nApaienHfi Melt) coboM, npercTasJbajy npolekTy-iyhe npaee. a ceH(a npojcfiIujj fioDKe.
Ha oaaj nauun aooujeHa npoje(quja ceH(e 3oBe ce (oca flpoje(uujallx xoca cnn(a (o{re.
22
IlocMarpajyh[ Molen u ceE(y yo.raBaMo:
l. Aa cy c€nRe naparctHxx ,lBnqa Mebyco6Ho rlaparerfie Il jeaHa(e.2. Aa cBe rrBuqe Moaera u ltBrirle ceHr(e Hucy jeaHafte,3. ,{a yraoau (oje rpaae riBratle ceHl(e nucy yBer( npaBr.OaHoc fi3Meby rjBrua MoaeJra fi fiBtua ceHkr, olHocHo x3Mehv [DaBeBe,trqnHe ayr({ E l5eBe- xoce npojcftuuje je xoe{aqnjenr cir]raienaI ooeJrexaBaMo ra ca g. ytao Kojx rpate ]paUr Ha 3 Ay 3oBe ce vrao
cxpeTarba, {oJe heMo o6e,lexaBarr.r ca c. OA BenllqljHc r r,,ia " , nr.i"n.crpahena 3aBlcll re[orJ {fi3fneq) koce cruKe n leonoar"r"noa, *o'r,iiovi _qlije, na ce oOrqHo y3[va Aa je a:30o,4b',60", 120"
Haj,renute c,rlre ce lo6,rjajy al(o je c-Ao" u 4 1..'2
3a4aran: Koucrpyrrut l(ocy cnlrxy l(oqlre uBuqe 3cm, ako je jeaHa
rheHa crpaHa napanerHa ca DpojeKTsoM pa tiu, a q: I , I,l n 30",
l:L' t"ry" npojcftqnie "tu ""pt"*ur"n noror,.j ?,, u *ou*yqrjjy Kocy crrry rpe6a (oHctpylcaTn nocraanvo la ,reNr.r v
xopr.j3oHTarHoj paBFn ,lcllpe i, Taxo ra cy joj 4ae 6o.rni:crpate rlapanerHe ca n,. 3aMlicnrheMo ra cMo paBau ,rr 060-prnH ol(o oce .r DaEuxe, Ta(o.aa ce ro(ralla ca 7r. IlpaBall3pakoBa orpeheH je yr,rov rojl qnHH ceHKa ca n-paaour r,locoM cjrI{e,, H o4flocoM xojr Docrojtr [3Meby lyxxHe ceHken ayxrHe l,B Ue KOUke, ,Ila 6hcMo t<oncrpylcali Kocy cJlnk)ftoq(e norpe6Ho je aa noncrpyIrruer,ao i6cy clury" BerruicrpaHa, Tj. KBaApara y pa3rirrM rroJroxajraMa, T6 ce toHcrpy(-q{Ja cBoa{ na roacrpyrqnjy ftocxx c!,ruKa lrsxoBEx reMeIIa.
floByuruo npasy ,r o6pnexrMo je ca r-1o je oca npojcr(-uule. rcnon rLe HaqpTajMo raaapar AoBoCoDo raxo aa jeJeIraH nap cTpaBt,lua napaJeraH ca r-ocoM, Tai kBaDpaT noe!_craB/r,a ocHoBy ABCD xouKe o6opeH) y :r,. h: ieveni cenoByl(y qoMane Ha nr, xoje he cehl, ocy .t. I43 BeruqhHe Aa_lor yara qlraMo !a npojeKryjyhe npaie Mory aa aora3e cqecEa oro3ro y cMepy neBo EaE xc. 3aro heMo u3 TaqaKa Hax-ocr y paBEu Jr. ficnoA oce t rloByhll [orytrpaBe noA yrnoM
oa 30' npeua ocr x. 143 lare Ipa3Mepe c(pahefba q:, ,turaMo
Aa Ha cBar(y ry nony[paBy oA lreHor noqertE Tpe6a DpeEerx no,ro-BEEy Ore 04 noMeHyrBx HopMarE'x AyxH ca Kojoi noJynpaBatMa 3aJenFu'{(y taqxy Ha oc{ ,x. Tako ce ao6llajy r<oce c.irteA, B, C, D.teuesa A, B, C, D, a ibItroBr4M cnajaEeM qerBopo-yrao ABCD:, (oca crrr(a &Ba{para A8CD _ napar"no.p"".
-Iy'.
Trx Taqaxa, TeMeHa laparlenorpaMa, noByt(y ce SopM€]re Ea ,r
^ ,:+.+,+,+
;.t;
06()-Ba4
keI(y
K-
lceIa-,ecLHA
EVO
BA
KE
143
ocy n dpenecy trytr(t4Ee uBtqe llolll(e;JlrMe ce ao6xjljy octarareMeHa r(oqre y xocoj cnuqu E:, I;, G, H.
BoqHe crpaHe ABFE n DCGH, noEro cy napanefire ca
n, npojenryjy ce y xpaBoj BenlrqtElr, rj. y KBalpa'e ABFEIr DCGH, I(ojn cy fioryrapdlr ca iGaaparoM ABCD. KocccrrlrI{e ocTarr.rx crpaEa HoIIKe cy kocoyrrlu napa!'Ier'IorpaMrr.flocMarpaj: I{a(Be cy Meby co6oM Koce cJI t(e HacrpaMHtrxcrpaHa r{our{e? 3auro cy aexe oa t6 Y npaaoyrJ a apyreHOCOyrJrff napaJerorpaMu?
BE)I(DATI,A1. Tacxa ce nara3t y xoplr3oHTa"rEoj npojekrlloi paBliu. fae ce
Ha.!ra3e r6eEe DpoJeKqlriel
Taqka ce HaJa3t y BeprlKarEoj flpojexrEoj paBEt. fae ce Hara3ebene rpojekqxje?
Ayr( ce Harara. ) \op 3oBra,rHoj npojc(rHoj paBH . fae ceHaJla3e t6eHe trpoJexur{Jel
4. Ayx je napaierHa ca BeprnKaiHoM npojel{TxoM laBHu. Koja jet6eHa npojekUuja Beha?
5. Haupraj npoje(u jc Dyxu fi oopPrl i6PII no,lox{aj y npocropy,aKo je:
L AB A(3; 0) B(2; 3) A,B,:1,52. CD C(4;3) Dil; 2) C,D":33. EF E(4;0) l'(4; 4) E,&:04. eH E,ot 4) 1J(3; 4) H.H":2
6. Ha cnuqa cy aare [pojc(uEje ayxu Oapealr l5rrxoB rloroxajnpeMa tlpojellrlrlrM paBHnMa (rr) n (tr).
B"
^'i/si io'
u'l v'
7.
Cn. 40
Haqpraj rocy cJjlrl(y r(Baapa
qeiry je nBuqa ,,d" Ha ocn x,
tr o6e oproroHa,rHe npoiekllnje.
(a:'cm, b:2cm, c:5cm) rpu
o:30" r q: a, a aarr.ru naqpraj
21
8, Haqpraj orrordHarH€ npojexquje s ftocy cJrxky rlrrre [xMeH-snja 4:25ce. b-15cm v c-7,5cn y pa3u',-px l:5 a(o jeb)lt. s.:45 u o: 2,3Oproronaana npojerqrja y yopu3oErarEoj npojefirHoj paBHn jel(BaApar crpanrqe a -4cm, a y seprtkarxoj npojexrndJ pasriunpaaoyraonkx nrcune 6,5cm. Ha(plAj (ocy catxy rcra reaaaro nexfi y xopn3oflTarHoj npojexrnoj pannr.r npl' qevy je d lx,u:30. n q- -.Ha crrrtrr 40,. aare cy rpojerulje koqre lr (Ba!pa. Oapeafir+uxoB ronoxal y rpocropy y oAdocy Ea apoiexrBe paBsi lrt n n!.
t0.
%,
H,i
Cn. 40
E\leri-Eo je
E{ jeiABHI'I
Te,!€d x,
lPeanVI. NP143MA
1. IIOJII,IEAAP, I}PCTE TIOJ'II'IEIPA
flo,rneAap je reoMerpnjcxo rero orpaHxqeHo paBHqM noRpruuMa.
MHorovr,lx liojfi orpaHuqaBajy nonnelap 3oBy ce crpaHe rrolrneApa.LtpaH ue Mrioroyr,la 3oBy ce nBnqe [oJ]ueApa, a reMefia NrrroroylraBp\oB! noi llc Lpa.
.p__, l__
Cr. ,U
nlA \o'r r r.ji JBa Bl\J n.,rh_!aa. a Hi rF^Jr'1 .5. oBo . f Hr,: rc ce il|jaroraia r,o.rr,edpr fBlI, I(D c1.4]'.
Ar{o norlle4ap fipcceqeNro Belioy paBfin llo6lthcMo nBoroyrao rrojq.:3oBe npecex nofiIre]]pa (EFG cr.41).
Ilonrerap Mopa rlrarq HajNratrc rrerupr crpane. Iornelap ca uerupr.t:ipane 3oBe ce lerpae4ap, ca xer cTpaHa lexrae4ap, ca uccr xeHcaeaap,
. ocav ' rpzHir or'la(.t:tl' u d. -Koje xe(cacnpe 3fla ?
2. TIPI,I3MA, BPCTE U OCOEI{HE I]PI13r\IE
, IlprsMa je flor'rncAap r{oa fiora cy .qBe crpaEo noAyAapdn x Mebycooolr napareJrEx MHoroyrnx, a ocTa,rre cTpafic cy napa,'refiorpaM!.
26
ABa napanenBa MHoioyria $By ce ocHoBe rrtl| 6ase npulue, a na-paJteJrorpaMn OoqHe crpa8e Dpu3Me. l-4a[ue koje orpaH,JqaBajy ocHosy3oBy ce ocHoBHe fiBsue, rpeceun 6oqH{x crpana np[3Me cy 6oqae tBtrrra,PacToja6e tr3ueby ocHoBa opr3Me je sucfiHa npt3Me.
cL 42
Koa rIplI3Me ce
a) flpecer koju(F Ea cn. 43).
6) flpecex roju(F' Ha cr. 43).
JaBJbaJy pa3J1{q&Iri npeceqt:je napanerad ca ocxoBoM 3oBe
Cr 4{
ce I|apanerrau npecex
C,- 43
je uopuaaan Ha 6oqle rBrqe, tropMalrrrr npecex
B) npeceft koj{ npona3x Kpo3 lBe HecycellHe 6oqne rBrqe, 3oBe ce!{jarotrilJrEr.r npece( (O rja c,t. 43).
3. aPcTE IIPL|3Aa'!A
IpcMa 6pojy crpauarra ocHoBe, npr.r3Ma Mox{e 6uru rpocrpaua, .rer-BOpOCrpaHa. trelocTpaHa, uecTocTpaBa qu.
I
,(a .na je npusua npaoa urtrlt t{oca, 3aorrcu oa rora aa ,r cy 6oqreEBEqe EopManEe rrJrrr (oce npeMa paBHr,r ocnoBe. flpaaa npu:ua je onar.sie cy 6osEe i.rBnqe Hop anHe Ha paBaH ocHoae.
IIpaBa rrprlsMa, r(oa r(oje je ocHoBa npaBrr'rar Mnoroyrao 3oBe cerp:rBf,,rEa npr3Ma. Ako npr3Ma IlMa cBe cBoje DBrrqe jeAEar{e (ocuoB]ie {6oqEe), oHAa je ro jeAHaI(ouB{qHa npll3Ma.
Qereopocrpatte flpy3vF r(ojc 3a o.uoBy Majy napa,tejorfart toBy.e'rapa-rere[},ne!8. napa,lc,tenrnear Hon l(ojr\ c) 6o,rHe He ui Hoptui,rrresa ocEoBy cy npaB[ fiapa!'renenune!II, IlpaB napailerenrnea Koja 3aotEoBy nMa npaBoyraonuri 3oBe ce npaBoyrn! napanenen{rrea.
flpanoyr,rt napareJrenurrea r(o! trora cy cBe crpane r{Baaparn 3oBece goutra.
Oco6uue npnsve.
l- CBe 6oqne fiBrlqe cy napaJrerne n jeaxa(e.3aruro?2, OcnoBe npu3Me cy noayaapHn MHoroyrJru ca napalreJrnuM crpa-
Ef,qaua.
3. Eoune cTpane ro4 npaBnJrne rrpu3Me cy fioryaapnrr npaBoyraon[rl!,4. Blc{qa I(oA npaBe np}.rc e jeAna(a je ca 6o.rHoM r.rBrqoM,
l.
2-
3.
BE)I(DAIiTA
a) Ko"rrl{o rrBrqa jtMa r{oq(a;5) napafienenrine!?
a) Ha MoAery npaBunEe rpocrpaHe nprr3{e;DOI(a}I{r ltUMofina3jre IlBurIe;
5) To ucro lIoka)ih rI Ha Moleny IIpaBnJrHeluecTocTpaHe npll3Me.
Onpet .e rrrr tHe yrJtoBc ayenpa o6paro-
- BaHe 6oqH CrpaxaMa:a) trpaBDJHe qerBopocTpaHe np 3Me:6) npaBnnne rpocrparie rrplr3Me:B) [paBnnHe llecrocrpaBe npn3Me,
Fl
cCr. 45
I Ha c,rvql 15 je npeacraB,beHa npaB JHa {!ecrocrpa 'a nplrva,O!pe.D}l:a) cBe nBnr{e, napane.lHe ca uBur{oM ArBr;6) cBe [B{qe, Koje cy M[Mo[na3He
ca uBllqoM AB;ca uBrqoM DD1;
5.3a I(ojH flpecek ka]xeMo Aa je:a) napare"raH fipeceK rrpn3Me;6) rnjaroHa,lllll l]pecek rpn3Me?
28
6. l4Br(a npsallrne jeraaxouwrulle rxealoclpaie npr:ue je 10cm.fJoei,rl .pa a/JrroI ric np rve x r firror rencrra t 3paq) HajILIIXOBe IlyXUHe,
CIAB3llgTocEoYo!
Ep(i
EI'I
Kao urro cMo npeltcraBuJtlJ Itoqfiy u l(Batap,npojeE4rijaMa ri Ii,LIxoBoM l(ocoNl c!'IIlKon, ra ].lcrrt
12.
It.
7. l43paqyHaj auMe[3nje npaBoyrnor napanenenrneaa aKo cy oHenponopu iorraJHc 6aoj"B va 2, 3 6. ,fJ ja'oHa.la nJnnrcren ncdrnyra je 35cm. (yryrcrBor 3a aLtMeH3IIje kBaapa y3i1Ir a-2ft,b:3h u c:6k, rre je ft ftoxcraflTa [ponopnuoHafiHocru.)
l,i3paqynaj nnjarona,ly ltou(e ako je rbeHa nBlrua 10cm.
AujaloHana l{oql(e je 34,6cm, Ko,rtrl{a jc l6esa lrBrua?
Kpor 1oq lipajrt,, rdqhp B'ruJ rourr^ 'ruje ru,la rc l re{eHJ ,4nocrrBfMU lerHl pJBdH, I lc i:r)o,l -ra JP npe.eh leaHJKoc PJh 'laHrpoyrao-
Ilo(a3arr.r. !a paBaH l{ojy orpebyjy cpealrurHe rarrKe rpII y3acrotHefiBr(e Kolc ce He IIaJIa3e y IrcTol paBltl,l I{oql{e, ceqe Koqlty ral{oaa je npecek IIpaBumH [re{]royr-ao. (y[yrc-rBo: Ha[praj KoqkyAB' Dl I Cll I I {v,r nJ c) rprl ) rircronH. Bruts hoe .c Hr Ha_jra3e y ncroj paBnfi,48, lF n IlG. IbuxoBe cpernHe cy reMerarrecroyrrra.)
llo(a,r.I na c. ) jprHov nap re._, n ncly 0]x (oie cn rjJj]cper le !ErjJ n:lpare,. \ B da .Kolc e npqrlJqajy ctoj60qHoi c'nJHrJ, ce'{y \ ctoj T rqHr, llo,{alar ra jF oBd ra,trrJ,ra'{l{a fipece(a aalaroHara.
13. t43paqyHaj roBprnnHy tujaroltar'II]or npcceta DpaBoyr!'Ior napar''Ie-
Jenurreaa Lr[je cy I1llueH3flje ai:5em, b:3c.n, c:4cn.14. tl3pa.JvHaj noBpnrr'rHe aujaronaJlElrx rpecexa npaBur''IHe ulecro-
crpale npr,l3ire ocrloBlrc rlBfiqe 20cm u BEcIrHe r5cn.
4, IIPTAIbE IIPI,I3ME
aBeNra oproroHarnnMHaquIt MoxeMo rlpea-
8.
(410-
BoCn- a6
II
H' E'
29
cTaBlrTrr rl Ma Kojy apyry np]BMy, Ha crrqlr 46 npeacTaB,beEe cy xop]l-3oHra?'rHa Ir BepT[KaJrHa rpoje(t]nla npaBe qelBopocrpane npn3Me Hola 3ao.HoBy lrM'r jcaHakokpar.I Tpane3 a ocHoaa joj ,1.)]{4 ) paBHr rr,y oBoM rrpfMepy je yrao c(peraba o-45", a koefnqujeHr ckpafruBalba
1q- . np qeMt, c) nBe cTpaHe nptr3\le flapaJlfJIHe ca BepTrrl{aJ'llor'l2
DpojexuioM paBHn.
FIa cJr.rqfi 47 faqpralra je npaBItJIEa urecrocrpaHa npn3Ma ca ocso-BOM y xOpn3OnTanHOj npojexTHoi paBHIr, TaI{o aa cy joj aBe cTpane na_
t' d'al cl's"
l. Haqpraj oprorolanHe npoje(qfije n Kocy c,ruxy npaBu,rHe qerBopu.crpaHe IIp]'3Me ar(o je 11:3cm, H:5 cm, u rorar{o lla je paBaEoc oBenapa,lerlHa cd pasH nrl,l otr Hre vra?'beH, 2cm. llp'r3Ma j. npt-CJloricHc y3 faBaH nz cBojoV 60,tHov ctlaHoM, yrao cKpetatLa
1a:30' r{ Koeorq ieHr 4- - .2
2. llarrpraj oproroHarrre. npojekquje n (ocy crIIlKy flpaBr.rnHe rpo-crparie npr3Me, a(o joj je npellna 6oqfla crpalra napaaerHa care \AarbeHa on rhn 4.fl. OcHosa rip JMc J. naparlcilHd ca jr'r oa r6e yaar'beHa 1,5cm. ycfioBrr qpra16a cy a:2,5cn;1]:3,5cn;
a:OO' ,, a: 1.,2
oB. RC'c.C.t. 4l
pare?'rHe ca B€prrnafiroM [pojei{rHoM paBnn, nplr qeMy jc y3eTo a:30oa.!:112.
*iF'c'iE'
30
4.
5.
Haqpraj oproroHante npoje&qnje u Kocy c;rrjxy npaBe np[3MeKOJOJ Je OCrrOBa laAHaKOI{paI{li rpane3J flapaJrena! ca paBnrr Jlrn oA rbe yaajbeH J,scrn. Eo'{Ha crpana npu3Me bH je naparerHaca n, ll oA r6e y,qa"EeHa 2cm. OcraJrri ycfioB{ lpra}ba cy a:4,2cn,b:2,8cfi, .:2,2cn, ll:4,icn,a:45 t q: ?-.
flpaB[,rlra uecrocrparia nprBMa Jrex! Ha 6o,]Iloj crpaHn napancfl-Hoj ca paBfiu n, u o,q tre y4ar'beHa 3a 1,8cm. Ocuoee npnaue cyflatajreJrfle ca n2; ropba ocHoBa yaalberra je oa nr 3a l,4cm.Haqpraj joj oproroHarrHe npojeKqnje n kocy c?'Itrxy aI{o je o-2cm,
IH:4,2cm, 6:30o u q- , .,)
i'2
6. JeaHaI(oIlBIlqEa uecrocrpalta npr€Ma Jret(fi cBojoM ocnoBoM y pa-BH rr, l_beH HajBFhH arrjaroHaJHu npeceK napaneilJII je ca nr,
oa f6e ),xaLbeF J.8cm, Haupraj ILPH. opTofoHaide npojFHu14lc
Kncy crltr{y, axo jc d 2.0r. cr 60" 'r ./ I .
[recTocTpaHa [pn3Ma npncnoBeEa ]epaBaH 12' a ocnoBe cy Jol napanenHeyA3.6eHa je an 1. 2cfi,Ilarlpraj bener(ocy cJlnkY ako je a:3cm, c!:60' x
r(oja 3a oc oBy16eroBux crpara
Je!sallolrBnqra npaBrrHacBojoM 6oqFoM crPanoM Y3ca paBrin nr. aoE,a ocloBaopToroHar'rEe np0Jelqlle u
5. MPE}I{A I' IIOBPITIlflA IIPI,I3]I[E
y neroM pa3peay cx yqxo !a ce Mpexa kol{ke ao6lrja pa3BujaheMcBux rpaHllqHnx 110Bpmu (oqfie y pSBan leallc o! t5eaux cTpalra.
Cn 48
Pa3BljabeM Moaerla rrpaBe serBopocrpaEe np[3Me
'{Ma jeirHa{oKpaH Tpan(i rc,'r, 48) y paBan jeaHe o4
ao6ujaMo Mpexy npeacraBJherry Ha cnlrqn 48,
npu3Me. Al(o rroBprxlHyca ,4{) odaa je noBprnnna
3l
Ha cn.49a npe^craB,'beEa je Mpexa npaBtnHe rpocrpaHe nptt3Me,a Ha cn, 49b Mpexa npaBnfire uecrocrpaHe npn3Me-
36up noapurana cBxx 6oqHa\ crpaHr np/3ve je noBptxqHa oMoraqanlr3vp. '16l,lp noBpLxr{rie ovora'ra noEpuirrHa or-nosa je noeprurrna
Cn. 49
ocHoBe o6e,rrer(nMo ca B, a noBpnlnHy o olaqanpr'r3Me P:
P:28+M.OBo je o6pa3aq sa ri3paqyHaBar''e noBplxuHb npr3Me. I43 MpexeIIa le noBpLr Ha oMoraqa leaHaKa noBpul H npaBoyraoHrRa.ocroBfiua je4Hafia 06 vy ocnoBe np lvc, na ic ,ll -O H, t te je6poj o6lrMa ocHoBe, a H Mepfl]i 6poj BucLIHe nplt3Me.
3a,qara( 1. I43paqyHaiTe lloBplttfiHy flpaBllnne rrerBopocrpafle npn3Meal{o je B 64cm, a H l2cm.
OcHoBa npaB nHe qcrBopocrpiHe flpx3vP je KBanpar, na rtMlMorc ie a2-64, rj. d:8cmM:4oH:4.8 12:384, rj. M:384c'l'2, a xal(o je 28:l28cm!P:28 + M -l2a+394:512P:512 cmz
3aAarak 2. l43paqyHajrc noBpru Hy npaBfirtHe rpoctpJHc npHrMe al{o jea:4cm v H:'cm.
OcHoBa.npaBtr,lHe rpocrpaHe npq3rtc je j.auaxocrpaHrqaHTpoytao, na le
{r'ii 16. t.73u ;"--::" " -4.t.73 6,92
ceBAUquja je
O MepEn
32
3a,qarar
3aaarax
B - 6,92cm' a 2B-13,84cm:.
O6rrr jearaxocrparrrvHor rpoyrra je 3d, fia je I\I:3o 11::3.4.5-60, rj. M:60cn', a DoBprrrHa rpu3Mc
P-28 l,4t e lli,B4a60-73.84
P = 73,84 cm,.
3. !43pa,ryrajTe floBprx]rny npaBr{rllie lrecrocrpaHe xpu3Me ax ,je M::J60 cmr a H- l0 cm.
KaHo je o6nM ocHoBe 6a uMaMo ra je M:6aH. l4z oeeM 360jeaxaxorrr c,1e0r !a je , Off n iO 6. ri. .r- 6cm.
- ^ d"vJ 3 36 L73
B- 93,42cn' a 2Be 186,81cn'
P:28+M ^,
186,84 f360:546,84P = 546,84cm?.
4. 14rpcqvllrj nnBf,utllrry rrpaBc qclBoPo.rpaHe -npNrue
xoja -aocHoBy nMa jetHaHoxpa(n rpane3 ar{o je d:3,6cm, b:2crn,, I,7cnr n H 1.5cm. OcHoBa npfi3vp jp jcnHal(orpal{I rpanp'l
Ina je B la b) h. ,Lla 6'rcMo 3lacyHa,lu noBpruHH) ocHoPP
norpe6Ha ;a je BIrcuHa rpane3a.
n",,ffi,,TJf X?#,?;"
.:""-(+1.h,- 1,7" - (9e-]i .
C]]- 50
rpoyrna AED, (cruka 50) npnMeHoM
!\
h,,_ 1,7' -0,82
h, _,2,89 _ 0,64
h ._,tz%
, - 1,5 cn,lr
na jc B '. (a I b).h - ' .(3,6 F2). r,5'221
B - : 5,6 1,5- 2,8 1,5 -4,20, rj. B-4,20cm2 a 2B-8,40cm,2
rl: (a + b +2 c) . H :(3,6 +2+3,4) . 2,5:9 . 2,5
M:22,50 cmz
P :28 + M :8,40 +22,50:30,90, lj. P:30,90 cn,.
BE}I{EATbA
L Haqpraj Mpex{y u n3paqyHaj noBptxlrHy npaBnnHe qerBopocrpaflenpa3Me aKo le:L a:2,5cn H:4,5cm3. 8:2,89cln,, Ll:scm
2, Haqpraj Mpex{y u ti3paqyEajnpr,r3Me aKo je:
1. a:4,5cm, H:6cm. 2. H-4,2cm, M:18,90crn,.3. ,8:1,73cm,, Fl:scrn. 4. M:108cm., a-lcm.Haupraj vpexy x u3paqyuaj noBpltrnry [paB[Jrne mecrocrpanenpfi3Me aHo le:
a 2cm, H .4cm. 2. H- 3,5cn, M-17,50cms.
B:10,38corz l'l:3 cm. 4. M-43cm2, a:2,5cnt.AtMem[rje npaBoyrnor napaJrenen[neaa cy: lyx{llrra 8m, rutp{Ea4m i BlrcuEa l2m. tr43paqyEajre:
a) rloBpln{Ily oMoTaqa,
6) rlnnqy xoqre koja 6r,r uMana ncry noBpuruny kao E flpaBoyrntIrapa?leJrelInIIea.
5. Kon Ka je B}rc{Ha fipaBfirHe qerBopocrpaEe flpnrMe, ako je oc-HoBHa tBllua d- 4cm x yx)nrra noBpluHHa P-80cots?.
6. floBpIIIItna npaBBnHe rnecrocrpaHe nprcMe je 23,19mt. tl3pasy-nal Ayxnny ocnoBEe nBnqe a u BucLlEe H Kaa i9 H:\aa
3 r.onep,ja ar vIlI DBp.!
2. H:2,5clrl, M:35 cm,.
4. trl:16cm2, a:2,5cm.[oBprxrEy npaBrnHe TpocrpaHe
l.
4.
34
I'
7.
8.
JI{MeHa fiyruja orBopeHa ca roprbectpaHe rMa o6nxk npaBoytJlornapanenefil]rneAa. n3paqyrlarv r6eHe rp !xMeH3trje, (aaa ce 3Ham Je Aylt([Ha rpM nyTa Beha, a uqpqEa tBa nyra Beha oa Ell-cxHe, ,r aRo le y(ynEa noBpu[Ha ocTarax rel cTpaHa 576cm2.
Koluxo je xaproxa norpe6no na ce l3paae Mo]lers qsje cy vpexenpux€3aHe Ha crsux 6l ako cy np[rr4xoM x3pa[e ry6a i5'n Ma-'tepklaaal !\AMeH3uJe cy IaTe y qeHr Metp Ma,
Cr. br
9. ,n,ujaroHa,la D [paBx,rHe uecrocrpaHe rlpx3Me ri3rioch l2cm, arraba rrjarosara ocuoae 5cm, tl3paqyHaj nospruxHy re np{3lle.
t0. l-43paqyHaj trr.rMeH3rje npaBoyrnor flaparrenenrflera ako cy oBenponopqroHarHe 6pojeBnMa 2, 3, u 4, u axo je nerooa nosiruunaP:5200cm,, (Bsax 3aAaraK 7 Ha crpasu 25).
6. 3ANPEAII'HA NPU3ME
Benl,qrjHa npocropa Koju 3ay3{Ma fieko re,ro ooBe ce saflpeMntra renf,.3atrpeMf,f,a csa(or traparenetrrtreAa jeAEara je trpoltgBoly troBpurrEe
octroBe { Mepnor 6poja beroBe B{c[Ee.
. _3a npaBoyrn[ napaneJrenuner ro,je .oqrrnelno, ]ep le V:abc, t\eje db IIolpIIIrHa ocHoBe a c MepHh 6poj BrrcuEe trpaBoyrnor napar'rene-nnneaa.
floftaxuMo rra ro Baxu3a cBe npaBe napaJlene[rneae.
Hera je ABCDA,B, C, D.npaB napaneren!!eA (crfiKa52). MoNelro ra nocuarparnBao (ocy [pn3My ca ocnoBoMAA1 D1D Lr 6o9frou uBnrIoM AB.3anpexllna raKo nocualpaneIlp 3Me jeaEaBa Je SanpeMtHrtIpaBe [rpE3ue ca ocHoBoM Hop-Martot npecefta ,t1NPQ u nr-ca&oM MM.-AB.
yr-,roBx cerEopoyrna MNPQ G:dja je paBaE flopMarHa Ba AB, A,8,.DrCt v DC, cy npaBfi, jep cy io Harrl6ix yr.loou upaaux areaapa, nb
q
I
35
cnea| Aa je qerBopoyrao ,I{NPQ npaBoyraoq{(. 3aro Je lpaBa nprBMa caocHoBoM MNPQ fpaBoyrrrx napaneaeflufle4. FberoBa 3a;peMr.iHa je jeA-Ear(a npou3Bo4y MepnEx 6pojeBa rberoslrx anMeH3rja MMD MQ I MN,a rrcToM npor3Bo,ly je jeleara u 3anpeMlrHa aaTor flapanenenxBeaa.
OaaBAe crean aa jeV:MM. MQ. MNV-(AB. MQ\. MN, jep je MM,:AB,
oaar{,te cneall !a jeV:B.H Dpv qeMy je AB Me:B r MN:H.
3anpevuna cBake flptr3ve jeaEaKa je trpox3soAy [oBptxrse ocnoBex Mepfior 6poja l5eroBe Bxc[Ee.
Aa 6r.rcuo oeo noKa3ard [ocMarpaheMo 4na c,ryvaja.
7. 3ANPE]IIIIIIA TPOCTPAIIE IIPTi3ME
Hexa FaM je nara Ma kaKBa rpocrpaHanprrMa (crrfi{a 53). OrHa'rfivo ca lz ienl ra-lpeMuHy, ca B noBpltrHHy beHe ocHoBe { ca1"' MepHu opoj }6eHe BncuHe.
,flonyurvo rpoyrao ABC to naparcto-tpaua ABCD x noByU,tMo verspry 6o,rny rer-uy DD, Koja je napa,re,rtra u jiaiaxa ca aarerpfi 6oqHe rBHue AAtBBT CC, no6xheMonar'arlelenltnea. uH Je arlaroHarHrM nDecekoMBCC,R, noae,ten Ha ,qBe rpocrpaHe npr3MeJeaHak \ ocHoBa ll JeqHakfi{ Br'ctHa. Aso jeyl 3anpeMuila napanerernllera, oqAa cneaa aa
ie V-28H, u V: LV,, oaaurc
V:BH.8. 3AIIPEMI,IIIA BI'IIIECTPATIE TIPTI3ME
Ha r,nu ], 54 je npeACTaB,beHa nerocrpallanpr.j3Ma, AKo noByqeMo r{por jeaHy oa 6oqurx ueu,ua. Ha riprvep AAr, ,0xjaroHa,IHe npeceKe, noaeJl -n{ cMo Je Ha rpr rpocrpaHe nprl3Me. (Ha raj daqrElpx3Ma oI n cTpaHa Moxe ce floaenuTIl Ha 4-2 Tpo-clpaHe upmMe.)
Ogsaquuo uu 3anpeMrne ca Vx V, v Vtu anoBprufiHe ocHoBa ca Br 82 Bs, Taaa rMaMo ai je
''nPtxaxo je
ao6njaMo aa jeV:B . H.
. _- 2BH]e v:-
v:v,+v,+v",V:B' H+B,H +B'H:(81+Bz+Bs) H:
B:&iB,):Bz;
-_-\-'4\Bt z,
Cn. 54
36
3aaarax
3aaarar
l. flpeceK jeaHor Bacrna je jeaHakofipaxn rpanca. ,t[[MeH3ujerpani':a cv a-12fib-3m, h-4m, a nyxxHa sar na H b00m.
Konr.rlto m3 3eM,'be lrMa y I6eMy?
3atrpeMfiria cBa(e npLBMe ie V:BH.lloruro je oB4e ocHoBa jeaBakol{pa(fi Tpane3, flMaMo aa je
v- @lb)'h..H- ( t2+ 3L1 . soo- rs. z. 8{J0- 24000.
Y Hacnny uMa 24000nt 3eMJbe.
2. qerllqsa llrrnKa uMa o6nEk npaBuflEe rpocrpaHe [ps3Me.Ko,!'tka je rexaHa re IxIlnKe al(o je ocHoBHa fiB'tqa ayra 6cm,Ayxrna mnnre 4dm, a cfleqr(DIlqHa rexuHa qefltxa s: i,8g/cm3?
TexIHy HeKor tena tro6xjaMo Haa rheroB) 3anpevrHynoMHoxrMo cneuulDn,rHoM TexfiHoM, Al(o rex(xHy o6enexfiMoca T, 3anpeMnHy ca I/, a cneqntluvny rexnHy ca s [o6niaMo:
T:Vs.Ilouro je ocuora ose rl]fin(e jeaHal(ocrpaExrlaH Tpoyrao, uMaMo
v:nn:o'1n3 . n *36']'73 .40:s . r,73. 40:622,a
3aupeunra jeV - 622,8cm',T -Vs-622,8 . 7 ,a:4857 ,84T^,4857,84 gT
^, 4858k9
t
TTJIII
BE)I{1.
BATbAI43paqyEaj 3anpeMrEy npaBtrnfe
7. a:icm, H:7 cm
3. B:8lcne, P-522cm2
5. a:2,5cm, M:35cm2
I4spauynai eanpeuuny nparulle
l. a:4cm, H:5c1t3l B: 1,73cm'9, P :27,46cmo
5. a:6cm, P:21l,l4cm'3. I,l3paqysaj 3anpeMuHy rrpaBt,lltte
1, a:6cm, H:8cm3. B:2,595cM', P-23,19m2,
5. a:gcm, M:576cm' /
qerBopocrpaHe nprrcMe aKo je:
2. .14:80crn':, H:5cm4. P-238cmz M-l40cm2
6. a:4,6cm, P:56cta2.rpocrpaHe npn3Me aKo je:
2. M :33,7 5c'll,2, I I : 4,5cm
4. P-73,84cm", M:60c'i26. M:720cm2, a:l2(jr!rpocrpane npaaue aro je:
2. M:84cm2, H-3,5cm4. P:188,76crn,, M: l60cm'
6. o:4cm, P:323,04cme,
2-
4.
5.
,( 6.
7.
8.
9.
q1
Mo4e"rn reouerprjcrrr rera rpu(a3aHrx na callllr 55 rapa$enucy oa apBera. Konu(a je reri&fla cBaKor oa lnrx, aKo cy airMeE-3trje aare y qer tMerplrMa a cfleqll(bllqEa rexr-rxa apeera je0,74elcits?
<iCr. 55
)l{ennMo aa EarrpaBrlMo lrouxy or nrorre qksl(a npaBoyraonoro6JruKa cuja je noBpmuHa 8,64m". Ko,rura he 6ltTu ijBuqa Koqke?Horfika he 6arr 3a[peMrHa?
Aara je flpaBH,rrra qcrBopocrpafia flp iva qHja je :anpeurua80dfl3, fioBpru[Ha oMorala 80dm2. Ko,rril(a je ocnoeHa ueuqa?I{ornKa je Bncfida?
3anpeuuna lpaBoyrnor napajreJrenlneaa je 735cmlj beroBe alr-Men3uje cy nporropquofianHe opojeBlMa 3, 5 r 7. Konfi]<a je Ine-rona nonpuuna?
KoMaa MepMepaauiremrje 0,6m;3anpeMlltte?
Iflanxa qeasra rMa npece( y o6rlxy croBa T, fiao Ha ctqux 56.AlrMen3rje rra cauqlr iy Aare y r,auai-ruerpurlra. lbena nyxnna je8rn. I4spauyuarrl:
ava o6arn npanoyr,ror napare,reltltneaa qxje cy0,3m; Ir 0,8m. l{onriKa je crpaHr.rqa (oqKe r.rcre
a)6)B)
3anpeMlrliy rleruqHe tuunKenoBpll]rHy qentqEe IxtrnKe
rrenuKa 7,8aKo je cfleqrOusEa rexxHa
Cn. 56
l*ll
38
10. EeloEcr{I' Hacrin_rlxtBe 300m rMa rpecek Kao rxro je rpr&a-SaHO 4a CnUqU 57 y MeTpnMa. l4spaqy:dalu rieroBy sarrpelduHy.
ll. OAHoc nosprlltna lBe xoqre je 9-. Kr*ru 1" oaHoc rlaxoBlrx' ' 16nBrqa? ltaraB je olHoc riltxoBrx 3atpeMrrHa?
12. I{ora cy Ayra 4n, roprba rllrptrHa rr3Hocr 1,20m Aoria rl]uprEa0,8_m n qy6rna 85cm. (o.luro kg Bpounupa ctaue y I<ora arrothl l(poMrtlpa rexr 80kg?
n
VII. II14PAMIIAA
I{aE cBe HBr.jue jeaHor por,'ba fipecer]eMo je,qHoM paBnrr ao6ujaMonojrueaap Kojrl ce 3oBe nr{paMkaa.
Il pav ra je nonxeaap orpaulqeH jeaHov MHoroyraofloM noBpuu naeJroM polJbacTe troBpluu.
cn. 58 cn. 59
C.paHa flrpaM n" orpaHfiqcHa MHorov-ioM 3oBe ce 0cHoBa nfipa-ufi4e, a Bpr fo,ba Bpx n pa\1 !F. ,[.eo por,t'acre floBpttlr ulMehy ochoBeII Bpxa nfipall[Ie 3oBe Ce oMoTaq Iin'paMrqe oMoraq fir]paMr,rae. cacrojl cer'r3 noBplnu TpoyrroBa koll{ ce 30By6o,rHe crpane llllpaMfiae.
14Brrqc I(oje orpaHliqaBajy ocHoBycy ocnoB8e oBxtre, a npeceun ooqHIlxcrpaHa cy 60'rse Bxqe. AlxfiJla Hop-Mane oa Bpxa nnpaMuae ao paB{It oc-doBe 30Be ce Bacmra n}lpaMnle.
Koa nupaMuae Haj'leuhe ce cpc-heMo ca cfleaehuM npecelrnMa:
5
/Ii rl
;/ :
/ rjiz
-'j, l
Cn. 60
40
a) ocIIoBoM 3OBe Ce [apaJrenflf, trpecer 11 pa-
Itpo3 aBe secyceAHe BBrrqe IIIlpaMx4e, 3oBetrnpaMrae (q c,1. 60).
1. BPCTE fl}'PAlIlXAA
3aBricEo or rora, aa rtr.r je ocaora nlpautae fpoyrao, serBopoyraourII.) nupaM{la je rpocrparia, qerBopocrpaHa, nerocrpaBa nrA. TpocrpanatrtpaMnAa, Koia je lonueaap ca HajMarb[M 6pojeM crpaHa, 3oEe ce rerpa-elap, lxTo 3Faqx aa uMa qeTrips crpaHe.
fllpav aa ca JeaBaKnM 6oqd[v uBluaMa, l{oja 3a oc]toBy Iva npa-
flpecek fiapanerad caMtrae (% cr. 60).Ilpecek kojx npora3r.rce AtrjarotraJfl{ trpeceft
Bn/'ItrIl MEOrOyrao, 3oBe ce npaBfirHa nnpaMraa.Ako cy cBe uBaqe nfipaMnle jelruane, ona ce :one
trxpaM{Aa. TpocTparra jea}raKonBRqEa rurpaMnaa 3oBe cerpaeaap.
a)
6)
6)
jeAtraxonBns[atrpaBltJlaH re.
2. OCOETiHE IIPABI J'IHE NT,IPAMXAE
Boqne crpaHe npaB{JrHe nupaMuae cy jeanaroxpaxr lr noayaap[rjTpoyrnoBr.r. Brcutla 6o'iHe crpaHe je 6oqEa Bllcuria rr t arroreMa.IIoaHoNjc BrcrHc fipaBrirHe nl,lpaMfiqe j. y uenrpy onHcaHe r{py-)r{Hllqe oko ocHoBe.
t
iCn. 61
IlrrpaMnle cpeheMo cJreaeha rpll kapa(repucrtqHaKoa cBa(e npaBllJrrerpoyrna:
1. 6osEa crpaHa nrpaMrue Koja je anoreMoMayaapHa fipaBoyrJra lpoyrJa.
rlotreJbeHa na lBa no-
2. npaBoyr.tn ?poyuo .ruje cy crpaHrrre: BfictrBa nupa{rae, 6oqsara,jua fi r6e'ra oproroHaJiHa npojcKurja Ha paBaH ocHuBe.
3, flpaBoyr,u rpoyrao qrje cy crpaHnqe: Bltc{Ha n{paMraej oorrHaB',rciHa ,anoreMa) rheHa npojel(qxja Ha paBaH ocHoBc,
flocMarpajyhu Mo,4ere (xnqaHe) Ha cnlrqlr 61 npuuetryjcuo .ua jeoproro\aJHa npoji,(! ja 6oqHe xBxue jclHaxa nolynpeqHrlr{y on caHe
,,c,6
4t
Kpyxfllruc or{o ocHose. flocMarpajyhH cnrfiy 61 yocaBaMo aa je oproro-flaiHa npojekuxja anorcMe jeaHaKa nonynpeqdlky onucaHe xpyxHrue yocHoBr nfipau lle. Ako noce6Ho Haupra{o kapaxrepHcTfiqde rpo} rre Kao
Ha c{Iluu 62 BratMo aa cy naM aoBo"'bEa caMo aBa eJreMeHTa rIpaBIlIHennpaM le Ia 6[cMo Haunt ocTane.
Cn. 62
i
RE}I{E AIbA
Kaa cy cBe 6oqse crpaEe nxpaMlr.qe jeaEa(e? 3auro?
Ko.raxo sajsrure 6oqHLtx crpana uoxe na liMa jenuaxonsfiqHanrpaMrraa? 3aurro?
lllTa cy 6oqHe crpaHe jeaHaKottBtqHe nldpaMlrae?
llocroju ntl y npaB ,rHoj Irrpavuru raqka no,ljenraKo yaaJheHa
or cBnx reMerla? lae ce oHa llana3u?
Xaxar.r cy arely co6oM yrroBn koje o6pa3yjy 6oqHe nBlrqe npa-BntEe rEpaMrue? Koruru je rbsxoB 36rp?
OcHoslta usfiua npaBr,tHe qerBopocrpaHe nrpaM ,ae jc l0cm'a Iieua anor(Ma je l3cm. Koalta je Bric[Fa nspaMaae?
EoqHa fiB{ua npaBrJHe'JerBopocrpaHe ntlpaMlfae je 17^cm, a
A[jaroHana ocHoBe Je l6cm. KoJIUXa Je B[cI]Ha nupaM Ae/
OcHoBHa rB ua npaB rHe ruecroctpaHe II paMUAe je 8 cm' a
Ihefla Blc[Ha ll cd. I43pacyHaj anoreMy.
9. B{cu}ra npaBlinEe rxecrocrpaHe ntpaMuae je l2dn. 6oqHanBrrqa 13dn. Konltka je ocHoBHa Bl'rla?
OcHoBHa tB"qa npaBtnlle rpocrpalre llupaMdre je 3m, 6oqnal'Btlla 2m. Ko.rlxa je nlcuna nupaMuAe?
AnoreMa npaB[rBe rpocrpase nxpaM re je 2m. BllclHa I tr|.
Konl'(a je ocHoBBa l,lBhua IILrpaMriIe?
l.
4.
5,
6.
7-
8.
ll.
r0.
12. Vl3pa3:1' BucuHy trpaBlrrtHor rerpaeapa floMohy uBr[e d-
I
42
3. UPTAIbE nllPArrlllAE
Kor oproroEarHe lpojekr{nje 3HaMo aa je kapaKTepllclHqno to rnlonapar'lcrHfi 3paufi npojel<ToBaiba nanajy HopMarrHo Ha npojeKrHe paBHri.
HatrprajMo oploroHar-He npojexquje npaBrnHeqeTBopocTpaHe rlnpaMnae,qnja je ocHoBa napaJrenHaca xop[3oHTarHoM npoje(-rHoM paBH[ (nr), a aBeocHoBEe xBrrle cY napa-iIe?'IEe ca B€pTuxanHoMnpojerorroM paBE[ (rq).
OcHoBa he ce npojek-IOBaTU CAOjOM [paBOM Be-nllquEoM y paBH[ Jrr, a Brj-crHa nrrpaM[ac, quje je Do-aHoxje y npocer(y aujaro-flana r{BaapaTa, Tj. y qeH-Tpy onucaEe r(pyxnlqe[pojeKToBahe ce y ly raq-Ky. 3aurro? npojexqrje6oqlrrlx ,rBxqa he nexar{y 4rjaroHarr KBaIpaTa.
flpojerqfija fiupaMlrley paB$u 1t2 je jeAno(pa&uTpoyrao, 6oqHa cTpaHaBSC, oanocHo 6oqfle Bu-qe BS ir CS. npojeKryjyce y jeaHy ayx, I(ao uAS r DS. Brcmia ce npo-jeKryje cBojoM npaBoM Be-nIIqIlIioMj jep je napanenllaca n2, a ocEoBa nrpaMnae,ql,Ija je paBaE EopMarl]aHa ne, y Ayx koja je ocqo-Brqa Tpoyrna. 3a oproro-EanHy npoje(ql]y rlpaBlrn-fle nrpaMrAe AoBoJLIro je Aa3gauo beEy ocHoBHy nBr.r-qy u Bxcufiy.
;
Cn. 63
AI(o HaM je [o3Hara boqrra rrBxqa [up{MuAe, oHAa rpe6a r(oHcrpy(-qujoM oApeArtrri npaBy BerlrqljHy BucuHe. BrcuEa nupaMriAe jelHar(lx6oqHfix r]Buua lava nonnolHje y ueflrpy kpy'a Kojfl ce Mo),{e on carlt ol(oH,ese ocBEoBe. I{oA npaBtlrHe qerBopocrpaHe nnpaMuAe raj qeHTap Jrex'ly fipecer{y Anjarona!'ra ocHoBe. 3raq[ BrjcuEa rlqpaMuae SO (cn. 63) je Ka-Tera npaBo) rror rpoyr,Ta SOB qHja je I noreHy3a 60,lHa rBxua nrpaMuaeBS, a np)ra Karera noJr) npeqiMK onrcaHe xpy,r{Hr,,qe OB.
IiIII
iFhIr-f,ep,Bt-F!-l.i-i-i-L0-t-Ft-FEi.
FaaIfh
i
iII
IIi
IIIIIII
II
'I
43
Aro rpoyrao BSO o6pneuo oKo Rarele oB ao paBHt ocHoBe ao6u-hevo rpoyrao B'SoO. {lt,era je rafio t(oHcrpylcarr, jep ce cBo,aH H"KoHcTpyr{utrjy npaBoyrror 'rpoyria Ka! je no3llara xaTeTa H xfinoTeHy3a).Karera OSo rpeacraBJba tpaBy BeJIllqIIlly BI{cnEe ntjpaMuae
Ha c,rfiqfi 54 je npeacraB,EeHa Koca cirrfia npa8xnHe qerBopocrpaHeI
nupay.rae npv qeMy je a-45" fi q - _ .
2
Ocuoey nupavuae qpraMo y Rocoj crnqu ficro Kao Il KoA lnpl,3Me.
I43 no4roxja nr.rcune D lnpcceta aujarodana) auxeMo HopM€ry Ha
r-ocyI, Ila rboj oaMeplrMo Ayx(IrHy BxcnEe. To je Bpx nl,paMlrae S
AKo ry ra,rry cnojnMo peaoM ca A, B, C t,l D ao6lrhexo r,r 6oqneuBrue y Kocoj cnfiqu.
a
l4Buqe nllpaMliae Koje ce lte BI'IAe qpraheMo ncfipel(xaaEoM r[sujoM.
Ha cnEqn 65 llpeaclaB5edajnM oprorosa.ilEntt DpojerqtjaMancro je [peAcraBrbeEa npaBEnHa
Crr. 66
je npaBxrHa rpocrpaHa nlpaM !€ cBo'u kocoM cnxkoM. a Ha cJlrrl oo TaKo
EecfocTpalla flnpaMfiaa.
44
BE)l{EATbA1. Haqpraj oproroHa.tEe npoje(r-luje u (ocy crrlll{y axo je c:45o,
I4: - 3a C,te,4ehe nftpaMnle:
2a) I'paBIIrHy rpocrpaHy nrpaMuAy al(o je ,t:3cm, s:4cm,6) npananan rerpaelap ako je a:4cm, raKo Aa y o6a crryqaja
ocloBa nfipaMule.!exn y xopn3oHTarEoj rpoje(rHoj paEH{, ajelHa ocEoRrra ,tBllqa 6yae fiapanerrHa ca Bepr[(anHoM npojeK-TI1OM paBHIl.
2, I-laqpraj oproroHarHe npoje(qnje lr Kocy crrjKy ako je s:30",I
4: 3A CJleAChe ll[paMlrle:2
a) r,paBr,lHy ' (TBopocrpaHy nr'JpaM,r!J aKo je ocrroBHa IBUlraa:4cm, 6oqEa IiBITI{a s:scm,
6) jenHaKonBu.rHy qerBopocrpalry nrpaMr{Ay aKo je d:3cn, Ta(o!a y ooa cnyrrala ocHoBa nripaMule relfi{ y xop!3oErannojnpoje(THoj paBEu, a ra cy cBe ocHoBHe rrBr'rqe napaJrct'rHe caBepluKaJlr]OM npojeKrIlOM paBs!.
3, Haqpraj oproroHa?'IHe npojeKuje ,r (ocy cnffry aKo je s:60",lq: 3a cJleaehe finpaMilAe:
a) npaBrinEy rnecrocrpaHy [upaMLIIy axo je d:2cm, s:3crn.6) fipaBrrsy LnecrocrpaHy
nfipaMu,qy al{o je ,t:-2,5cn, s:3,5cm, rakoAa Y o6a cJlyrlaja ocHoBanupaMrle ?'rex[ y xo-plr3oHraflfioj npojeKrHojpaBnfi, a HajBeh[ a[ja-roHanHrr fipece& nrpa-MIlAe 6yae rrapaJrcJraHca BeprnEajrsoM npojeK-Tnoj paBnn.
4. MPE}I(A II TIOBPIIIIIHAIII4PA]\[I,IAE
Moren [ecrocrpanenupaMrae HanpaB,Berr oakapToHa pexnMo n0 ];lBr.r-rlaMa r{ao llrro le npur(a3a-Eo Ha cfl. 67a, uftr Kao nlroje nprlxa:ano aa crnqrl 67b.
3arltM roror{fiMo cBccTpaHe lfpaMrrae Taxo ,aaJre)xe y ficroj paBHn; ao-6ujeHe {burype ce 3oByMpex(a tr[paMnae.
I
Cx. 67
Iilt!o
o,tlsT
E
i
I
i45",I
lqajaE,aeK-
'|
;30",I
Iqa
FKOhoiacaI
p",
:
akooBaxo-dojlia-Pa-IAIJFr-I
L:tFeioa
F"
rbfo"
i"-pv
-
15
Cr 68
finpaMnae ocEoBEe
3aaarar l. Haqpraj Mpexy npaBurrre qerBopocrpaHe nllpaMllAenBlrqe 2,5cm r 6o,rHe nBur{e 4cm.
[,13 raqke S Iro,rynpeqHllKoM jeaHa-KnM 6oqEoj IlBltqll nupaMuAe 4cn onu-nIeMo ryk, u yoqr'rMo jeasy raqKy rra $eMy.O ryny oreopo ruecrapa, ftojr je ielHa(.rcrioBHoj nB[]lu, 2,5cm o6eflexfiMo jouroernpx raqr{e, y3acronHe raqke c{ojxMo.{yxnMa, a 3arnM rrx cnojllMo ca ra.rKoMS. Ao6ljaMo 4 jeana(oKpa(a noryaapHaTpoyrra Koju quHe oMoraq nr,paMule.
Ha jeanoj o,q rfix ocHoBa rpoyluoBanaqprajMo xBalpar clpaH!{e 2,5cm Il Toje ocHoBa nnpa.r,[fiae ,
Harrpraj Mpexv ucre nrpaMuae HaIpyru EarrfiH,
3aaarak 2. Harlpraj Mpex(y npaBfiJrne rpocrpaHerBnqe 3cm Ir afioreMe 4cm,
:'
!
I
llIHaqprajMo jelHakocrpaHuqaH rpoyrao crpantqe 3cm. [o6u-
jesn rpovrao je ocfioBa firpaMuae. HaljeMo cpe,quEy jeaHecrpaBr{qe rpovrra r y rboj ao4urHeMoaopna,'ry na ry crpasftuy, OrMeJ''rMoHa HopManV 4cm ,' ry raqKy cflojl]Moca l{pajlnuM raqr{aMa crpaHurle rarorrpoyrna. Ao6[jeH]r rpoyrao je jerHa o!6o.rHrrx crpasa nupaM'fae. Ha cBa(oMcrpaEuqoM jernar(ocrpalrllqHor rpoyrrar(oHcrpynurMo oBa(aB jeaEaKoKpaEurpoyrao, jep je cala oapebeHa n 6oqmr{Bnqa nupaMfae. JeaHal{ofipaKfi Tpoy-rnll flpeacraB"Eajy 6oqne crpaHe u qIIHe
oMoTaq nupaMllae.Haqpraj Mpexy Aare [npaMure Ha
apyrfi EaqnH.flocMarpajyhu EarlpraHe Mpex{e
nnpaMlaa yoquheMo aa je noBpullrHaCr. 69
nnpaMnre jeaHafta 36[pyparrnae.
noBpIIIUHe _OCHOBe
U nOBpIXIIHe OMOTarra nfi-
Axo [oBp]xuEy nllpaM]l,qe o6erexrdo ca P, noBptuxHy ocHoBe caB, a roBpunHy or{oraqa ca,M ro6rja ce o6pa3aq
P_B+M.OBo je oDllrrr.r o6pa3aq sa iBpaqynaBarbe rloBplxExe nlpaMIJAe, u3 (ora ceMo") ijBecru o6pac . 3a hJlaqyHaBarse nospuruHe nojetr/h \ nrpavrna,
3aAarak l. 14rpil\yHaj noBpu try nnaB .lHe rpor-TpaHc nrpaMx!e q,,jaje ocEoBHa uBuqa d-16cm a 6o,rHa lrBlrqa s:17cm.
P:B+M,
46
Kaxo Je yIIMAMO TPII
s
oBoM 3a,qaTr(y ocHoBa jellda(ocTpaHrqarr Tpoyraoi a y oMolaqyj-IHaKor(paKa I no,qy4apna Tpoyrra. oHAa jP
3a
Cn. 70
P- t'v o +3 ""423a x3pa'ryHasalre noBprufiHe HenocrajF Hav ano-TeMa, (ojy heMo ro6rir{ r'3 lpaLoyrror rpoy ra8,445 (cnul(a 66),
h'_s3 _ l: I _t7.- a,_289 _64_225\21
B h:,'l 225:15, ft:15 cm, na naa u y o6pacqy 3arfiparryHaBarbe roBpllrIlHe 3aMeHuMo IIo3HaTe Be-
P* 256 173 73. 16 15 -rro.?z r36042
P * 470,72 cmr.
3aAarak 2. Konnt{o 611 6u"ro norpe6no xapllrje y 6ojr Aa 6Ir ce o6relrlloMoaen o! KaproEa npaBirJHe qerBopocrpaHe nrIpaMrAe qujaje aloTeMa i:l3crn u BrclHa [lpaMaae H:I2cfil
ItaKo je noBpnlllHa cBaxe nllp€Mnae &3pa)r{eHa caP-B+M, a ko! npaBurlHe qerBopocrpaHe nxpaMll-
ne ocHosa je KBalpar. ro qMaMo P-ne | 4 0]rre je2'
P:4'+2 ah.
3a xlpa'{yHaBaH,e noBfr$nrre Ireno.raje HaM oc-HoBrra Brua Eojy heMo ao6urr fl3 npaBoyr?'rorrpoyrna O.4{S (cn. 67)
f: h2 _ H. _ 132 _ r2r: t6g _ 144:25
r:125, r:5 cm.
3.h.a
Xrll
I{aRo je
raBalpaTaCn.7lnory[peqHn( yntcaHe l(pyxmrqe Koa
r: ! *e111 Ea je a-Za2
d: l0 cm, Ila je
P : t0, + 2.t0 . 13: 100 * 260 :360
P: 360 crn'.
oorennnr xaproHcn Moaen norpe6Ho HaM jeAa 6ucMoy 6ojr.
I l)A/.ili, |\
'ot
t,):-;,
360 cm! xaprrje
lcy
Fo-rDrari
l3alDe-
Ii
!f,oLj"
r
I
I
iI
frtI
.E
4?
3alarax 3. I43paqyHaj noBplxtlny npaB[JrHe uecrocrparre nlrpaMnae6oqEe rtBllrc l0 cm r.r BrIcIIHe 8 cm.
P:B+M
- ^ d'V3 ^ nh ^ 3o,V3 ^P-6. q )6. z 'tJ. P: 7- I-iJ oh.
3a u3pasyriaBarte noBp ruxe florpe6fia HaM jc ocHoBFa nBltqa 4 tt aloreMa/r. Ocnosny rnuqy heuo r06lrrrj Ir3 npaBoyrnor rpoyrrla AOS (cn 72),a anorpMy x3 rpoj rna 8,115 (c,Ifika 72).
sR' _s!_IJ':10'_ 8.:100 _ 64:36
R: V 366 :6 R-6 cm.
l(a(o je norynpe.rHlK ,orrttcaEe xpyx(Hfiqe ot{olpaBnnHor lxecToyr,!a JelHaI( ayxnHlr ocHoBHerjB']qe, ro je /1:6 cm,
I43 rlpaBoyflor rpoyrra B,MS
x, -., - /.d \: y6. . 3, - 100- 9-el\21
tt': l9l a,9,53, har9,53 cm. Cn. 72
3aMenoM y o6pacqy 3a n3paqyHaBalbe noBpnlr e ao6nheMo aa jc
p = r.36 lQl3 6.9,53. 54.1,73 .t8 9,53
2
P - 93,42+ 171,54:264,96
P = 264,96 cm'.
BEII{6AE A
l. Haupraj Mpe,ky npaB ,lHe rpocrpaHF Ir paMuaP ocIIoBHe Bltde3cm 6o,rHe rB[qe 4,5cm, HanpaBU Moaen u r3pa,JHaj thPHv
noBprxnEy.
2. Haqpraj Mper(y npaBtJIHe rlcrBopocrpaHe nllpaMllae oclloBHeNeuqe 3 crl1 { 6o.rHe LIBItqe 5 cn. Hanpanr MoaeiMBpa'IyFajE erIY noBPlnIlHY.
3. Haqpraj oipe*y np""ton" ruecrocrpane nr,rpaMlrae ocHoBHe [BIr-qe 7 cn n 6oqne uBxqe 9 cm. Hanpael Moaen l,r fi3pa'Iynajn0Bpmrrdy Ilr'rpaMrr!e.
I43paqynaj fioBpulfisy [paBulrHe qerBopocrpaHe rMpaM]rae alo jeocnoeHa aslina 12 cm, a BncIlEa r tpaMuae 8 cm,
Konl1ko jp xaprrje y 6o]fi norpe6Ho na ce o6,renu npae llla uecro-crpaua nupaMfitra oinoeHe Hexue 4 dm u 6o'rHe [Bxue 6 dm?
i
48
6-
7.
Honllko je qpeloBa nolpe6Eo aa ce fio!(plrje kpoB l(oju IrMa o6J!]rknpaB JHe 'rerBopocTpaHe nfipaMunP aKo jF ocHoBlla Br.illa 9m, a
anoreva 6m, xalt cP 3Ha na je !a Im'gnorpe6Ho 15 upenoBa?
B[cnEa npaB]rrne rlecrocrpaHe nfipaMllue jc 8ln, Korum je noBp-LruHa oMoraqa nfipaMfile KaiI jc ocHoB}ra uBuqa 6n?
8. OMora,r npaB ,1!,e rpo.rpaHe nrpav ae je 45m2 Ko,rMXa je ocHoBnatrB$rla cKo jr av)rfllHx anoreMe 6m?
KoJ jKa je Bnci-iEa npaBrtjllror rerPaeapa qtlja je fioBplnffia lmt?
Xonul{o je mt raarHa norpe6Ho 3a 8 BojEn'r(ux [aropa o6JIIrKa
npaB .rHe qerBnnocrpaH( nxpaMxae. q/ja jc o.HoEda fiB ua 4ma anoreMa 2,6m?
10.
11. I43pa.ryHaj noBplrrlrHy npaBrnrle lpocrpatre nipaMlrae ano je:
12. I43paqyHaj noBprxuEy npaBunHe qerBopocrpaHe nnpaMule aKo je
2. a:1,6ctt M:8cm'4. B:0,81'dri" M:3,60dm'.
13. 14Jpa,r) Hai noBpLrJfiHy npaBurHe Lxe, rocrpaHc nlPcMxDe aKo je:
I a:1ocm s:lscm 2.H:6cms:1ocm 3. a:2,5cfi M:21,50cfi'
143 oBor ouleaa MoxeMo 3al{ilyquril aa je 3atrpeMn{a trtrpaMuae rpnnyTa MaBa oa SanpeMllne llpltsMe ca (ojoM f,Ma je4ral(y ocEoBy tr BncuHy'
1.4:6cm s:5m3. h:3,'cfi M:21cfi2
1. d:3cm s:2,5cm
3. h:2,5cm' M:8,50cma
2. a:2,5m M:75cnr2
4. B:l,73cnt2 M:27cm2
:
?I
!
,t:'l,i
II
3. 3AIIPEMIIIIA NIPA]I'IIUE
Bule.nrl cuo aa je 3anpeMuHa nprcMe ibyIrKLIItja Belre ocHoBe Ir BI{-
c He, JanpeMuea lP ) roJlhr{o Beha )For Ko cJ ocloaa r ^B'4c
Ha np jvP
Bphe. na n .e ro vo)Ke pPhr ra QnorvxHy n ldv flcl
,[l.a 6ncvo uspaqyna,u 3alpeMuHy nupaMlrAe nocjlynrutleMo ce jeA-
Tpe6a ualpanurt MoreJIe nplr'3Me rr nllpaMrlle jealia(lrx ocnoRa I'r
BrrcI]Ea. KaE KaxeMo jeaHal{fix oclioBa,MllcrlitMo Ha jea]ratocr lr,]lxoBrix noBp-IllI,IHa, a He LI O6J1'lI(a. TnM MOAefiUMa
oncrpaHnl,ro jeaxy ocHoBy ll rxynjLxHynrpaMUle HanyHUMo EonoM, lJ r o HJIM
necKo , na To npfrfiieMo y tllynJ'bl'fHyrrprz3Me. BuIeheMo aa je Boaa npertBe_Ba I13 nfipaMl4ae 3ay3erla caMo aeo 3a_
npeMnHe npl{3Me ff 4a jc florpebHa,Taq-fro rp't nyH€ rlapaMI{ae Boae tra oJ,j ceHafiyHrIj]a npt3Ma,
C!. 73
GE]trEr,jl
4g
To MolBeMo 3a('byqHrn n nocMarpajyht cnury 74.
PaBHlrMa otroehettrM raqKaMa ACE t AFE noqenxnt cMo np 3My
rcn- 74r Ho roll i;oc'rpoHe llfipaMxae. nrpaMH[e ABCE tt DEFA cy jer'nare, jip rnijv jeinaie ocnoie IABC n DEP) u Bttcttfle (BF H
-DA) At<o
nuoauraaua DEFA tr ACEF3a spx ylMeMo 3ajelHlrqxy raq(y ts' ra'!!a re
aai nrpaurrne uualy ieanare oclroee A CE u ADE fl BficlrHy EF. lep ce rpoy-in, o"tioea aonyroyly no npasoyraollsxa ACFD Kaxo je nupa-MHra ABCE
iliri*i t"iti"iqn bEFA, ro iy re rp'r nr'rpaMuae Metty co6ou jeanake
Kaxo ce 3anpeMfiEa cBatae np[3Me l{SpaxaBa ca
V:8, H.D
cnern aa Je 3aflpeMrr-Ea cBa(e nspaMuae
v:!n.u.3
OBo je onlxrn o6pa_3aq 3a s3PasydaBalse A3aIIpeMrige nupaMfiaeI,l3 KOra ce Moay s3Becru o6pacrl| 3a t3_paqyEaBa16e 3anpeMt'l_sa trojeluHux nupa-MIltr4.
3aAarax l.je
Ct. 74
lr3Daqvdal 3anoeMnHY npaBr'lnHe uecrocrpaHe nspaMI{ae aKo
".;.";, ;"rrd a -8im n 6oqna fiBuua s-lOcfl.
v: l-n. n
,r - ! . o ot''l g ., "r.
y- at^!9 . 11. BnaqMo aa flaM Helocraje'34"zercrHa H aa 6HcMo rpaqyrlarl 3anpeMl,tHy BficxHy nfipaMrae
H heMo [3paqyHaTx ni npaeoyraor rpoyrna AOS (cn /z)
Hs: h! - R!: 10, - 8!: 100 - 64:36
H:6cn
r s -l 6 64 1'73 .6-6.32.1,73-332,16034
v:332,160cm'g
3a,larafi 2. t4apalyxai sanpeunny npaBsnue qerBopocrpaue nl'paMxqe- n.nos'ue xnl,lue 4:l0cm I,t afloreMe ft' lScm
v: Ls.n. v: ! a'.H
4 r.orcrpxir s VIII P!3Pcr
50
l4s npaBoyrror rpoyrra OMS (cn. 71)
I'Ir :hr - f2 : 132, 52 : 169 25 : t 44
H:12cm
v: !. too. tz:roo . 4:3oo r-4oocm'23
BE)REAIbAl. Konr,{a jp 3anpeMHrra qc-BopoclpaHe n Pavtqe qrja ie ocHoeHa' ueuqa 16cm, a anoreMa 17cm?
2. l.3pacy1ai 3anpeMlEy npaB!4r'IHe uecrocrpaHe nl'rParrule Ko! Kojeje H:a:2,4cm.
3. Hor I{a je noBpBruHa ocHoBe nupaMxle qrja je 3arpeMlrHa 21,875m'gn BucuEa 3,5m?
4. llerua ,rereoporrparrc j^nHado cHqHe nxldv/4e jP,r,
a) I43pa3u roBprxrEy re rlupanftne Kao lby]rEquja nBII'rc r.l.
6) I43pa3u 3anpeMlrHy re nnpaMltae kao OyxEqlijy uBlrqe d
5, OcnoeHa nBrIIa flpaBnr'rlre qerBopocrpaHe nupaMuae je d:6cm, a6oqHa sB"r{a s:8cm, l43palyEaj rbeIry uoBprxltHy n 3anpeMlilly.
6. npaBnfiHa rpocrpana fiupaMl{aa IrMa Bxc}tEy 1J:8cfl u anore yft:l0cm. Hatu joj notsptluHy u 3anpeMtrHy.
7. t43paqyHaj noRp1nrlly I,I 3anpcrllrHy npaBnrHor rerpaenpa ocHoRllc
8.
HB&Lle d:1?cm.
lloBprxlIlla npaBnnHor rerpaenpa je 8l \l3cm'. KoJIr(a je H'eroBa3anpeMnEa,
3a ppvrrra npirBl],rHor rplpdcDpa ie I8ftcma. Ko,l Hn jP lLeloqanorpruuna?
10. l,l3pa.ryHaj noBprrLIHy '' 3anpeMtlty npaBurrHe qerBopocrpaHe nllpaMnae ar(o le:l. t1-2,4cm s:2,8cm 2. d-6cm h-Bcm 3. s:gcm H:scm.
ll. 3enp-M 'a npaB ,lHe 'r(rEopocrpaHe n pav rP je lJ5dm'!. a thellas fllHa 5dnr, Koauxa je tr,ena noBptu rl,i?
12. 14:pa.ylaj rclr{hHJ qe,l qHor P,rMera 06,1rl{a nlaB rHF qFrBo-
po.Tpa e nupa\4 de ocHoB'tP r,lBHue l0,m rnolcvF llcrn a(o jeineq drqna rcn{ Hl t..nrl(a 7,8g cm3
13. I43paqyEaj 3anpeMxlry npaEn"rEe rpocrpaHe ll]lpaMfile ocIIoBHeriBnrre lm u 6o.IHe IrBlqe 2n
14. l43pa'rymj 3anpeMlHy npaBnrlic lxecrocrpaHe nl{paMuAe ocIroBHer'rBfiqe ln tr 6o.rHe IlBIqe 2m.
".{
9.
15.
16.
5l
JafloeM}tHa noaBriHe uecrccrpaHe nkpaMHAe je 54[31n" 6olnacrpjna :al,rana ca ocHoaoM )rao otr 60'. Korkka je ocHoBHa uBflua?
KoMa] Mepvepa o6,1fi(a npasl,l,lHe uecrocrpaHe n paMrAe xoja,Ma ocHUBHv fiBnuv 6cm x 6o'{Hy I'lBI'tu} lucm rexak le672,624g. Ko,ruxa je rurona ,-neuaQuoua rexltla?
flpaBunHanBqqe 2?
a) KonnKri
1*.\
li
17. rrecTocTpa8a nltpaM[Ia gMa ocHoBHe uBfiqe o Il 6oqEe
yrao 3aKnana 6oqHa uBuqa ca ocHoBoM nqpaunaB?
6) lr3pa3 [oBplrtHy nl'tpaMl{aefiBgqe {1.
B) l43pa3[ 3anpeMlrlry nuPaMlaerB lle o.
l(ao {yEt(qrtjy r6eHe ocsoBlie
t(ao oYH*IIHjY bede ocBoBHe
18.
19.
y nDaBovrnoM naDare,renunetrv ABCDEFCH, !HMeH3 je AB'in.ii.'"" noonoitunonrn"" 6iojesava 3, 4 5. a q jaronara
ai r.rrnJ.un,It,Ixa ABCD l{3Hocd lm. t43paqyHai 3anpe lHynuorr!r.nitn".q". HauFraj lujaronane AG. AH, CE lr DF napa-
aeienrncna, llokaxx_ !a cY jetrflaxe { !a ce ce(y y ltcrolraqr(fi.s, oBe ariarona,re oapebvjy ulecr n paMllaa apxa s qftle
cy ocHoB' crpade napane,leninela. Ko,rlxa jc unpeurta cBaxe
oa ibrx) O6jacrrx pe3ynrar 4o l{ora c ilorxao.
l4MaMo kouxy ABCDEFCH t{Btrue 4. -[lpasoM FH xoja je. ar-ja-
roruna foolb; floBp'll Be I IeM€HOM A nponaJx paBaH KOJa 0A'
pehyjc nlpanruay AFHE Vlpacyqai 3anpeM{Hy u noBpr
I
Ii{ll
lr
'j!
{'l
ri,l; ,
l''l
VIII. EJII4TICA
l43peHtrvo o! KaproHa il! rHMa xpjxHy n'loqy. AHo y 15] rne4avoTAKO Aa HaM 3paK 3 Oka nana ynlaaHo Hd rbcrry noBful. a,l0ehcvo lc Hao
kpyr. O(peHeMo ,[Il xpyxHy nnorly 3a lrekf ylao ol(o cBol_ xopu3oEraJl-nii npe.rnuxa, oH he ocrarl-r rr aalbe ficre BcruqlHe, aor heuo sa sep-ruxa,xnr.r auatr yrlrcal( aa ce cMalr,'Io- Taaa heMo y],tccro (pyra BlrlerlljelEy roBprII orpaHuqeHy npaBrjrEoM KpItBoM nnHuloM I(oJy Ira3nBaMoe.nrria. Haleat, axo ce rpyxna njloqa ol{pelje 3P 90' BtaeheMo je xaoayx roja ie llo cBojoj Befitr'rflr! jcrHa(a npe'rHt,Iky nroqc
O@++Cr. 75
l,l Kp[B) n Hfijy eifinc] MoxeMn HoHcrpy carg Ha HcxoiHxo Ha-qlrHa, Mx he!lo ce }norHarfi ca HajjenHocraBHxj M Ha,rxHov. la6onfivofla ij3BecHoM pacrojar6y aBa excepqfiha (F1 n F-, cr. 76) y xaprujy Haxojoj xenrMo !a HaupraMo erlrIcy. y3MlMo 3arLIM KoMaa Konqa rI cBe-xnMo rberoBe (pajeBe ratso aa HanpapllMo oMqy. flpe6aqlMo yaBocrpy-qer xoEaq oxo eficepqriha, roj[ uopa 6nrr.r Behn oa l6nxoBol pacrojat'a.O,'roB(oM 3arerHrrMo KoHaq. IIoBraqeIbeM oJIoBKe qpraMo eruflcyr artr noaycnoBoM aa koEaq npr roMe 6yae yBex 3arerrryr (cn, 76), OBaKBo qpral6eeJnulce 3oBe ce uexaHxrlKo rlpralSe.
i
ir
i1Ca cn{re 76 Brlrr ce aa ejrrnca rMa
aBe oce crMerprije. Ayxr AB 3oBe ce Be'nlrr{a oca ernnce (AB:2a), ry)x CD M'.j,taoca envnce(CD:2b), a H,rrxoB IIpecel( raq-ka O [JETap errn.e. CsaKd !) x Hojaclaja aBe raq(e errunce lt npoJra3[ Kpo3qerrlap 3oBe ce trpeqE x enrnce. Taq(eF1 r F, 3oBy ce xf,xe errfice. OncrojabaMa xoje ra,rKe P, sa e $rcu, oA muxa 4
uIxojt
hererx
(py
!trca
Hexggtxpaca
je(
!i cEo!cr(p
BE
5a
/" 3oB] c, nore3l,l. O.o6rHa cixncp je ra aa ie 36xp pacrojarba Maxoje raqke o! )r(uxa c?a,raH 'l
jeaHax Be"rlllxoj ocn, Ti,
rt+tt-2(I'Koca c"rxKa (py)xnhu' je enrnca. OHa cc Moxe saqprarn aso ae
(pyxnrqa lr3Aerll HoMohy Buue flaparerHrix reruBa, qlje ce Ay)r(ItfieI{oco rpoJer{ryJy.
Ha4prajxo xpyxnrqyu npeqHrjK AB rlapa,renaHca J.-ocoMr n CDI iraHa ,r-ocy. 3ar&M noByqlrMoHeI(O?rnI{O TeTnBa HOpMaJt-Hnx. Ha -{-ocy. rbfixoBekpajrse raqIte obeJrer{{Moca l, 2: 3, 4; 5, 6; 7, 8.
flpc.rHn{k AB npo"lcr{ToBahe ce cBoloM npa-BOM BCJqqEEOM, ICP JC
il ca r.ocoM, a ctse reTuBedopMaJrHe Ha [-ocy nuahecI{paherbe.
Cnajaneu rauaxa A,1, 4, i, s; B; ny(oM ao6rr-heMo kprjBy kojy 3oBeMo
enmca, a npeaclaBJ6a l(ocy
BEt{EAnrAl. HaDprij MexaHncxn eJrr.rncy ca Be?rt(oM ocoM 2a:20cm v Mal\oM
ocoM 2lr-l2cm. XoJrrr .r Mopa 6xrn KoHaq n y kojoj ce yaa)l'eEo-crr o! rIeHTpa enflnce Mopajy yqBpcrnru excepqlhn?
2. Ilaupraj Hocy crrr(J xpyxHrue noiynpeqHlr(a r-2cm aKo jeIc:4J' A A:'7
3. Haqpraj Kocy
a-ti0" u q:
cruI{y I{pyxHArIe.
crlx&y kpyxErrle2
3
xonynpeqE[(a f -2,5cfi aKo ie
nonynpeqhrrr{a r:3cm al(o ie4. Haqpraj Kocy crrE(y xpyxHrqe
s-30" ttIs:t
t,! L
I
-
Ct. 77
IX. BA"'bAK
noBpur je oHa noBp.! xoja HaclajF xpelJ+FV noa.BP
o.'aje napa,le,lHa ca aBoJllM 0pBoo rh,'lM FoioxrlcvxojoM Hlrje y Ecroi paBIrIr.
flpaea xoja ce (pehe y 6tro KoM noro-xajy 3oBe ce ,Ll3Botrlliqa tnfi reHeparptca a
Kpu;a ro Kojoj ce npaBa l{pehe 3oBe ceaxpefiTplrca.
At(o ul,l Hro qHy noBptll t(old i( HarTa.niKpeTabeM t3BoaHLI[e nO AllpexTpncn l{ola leKpyxnBIIa, fipeceqeMo IBer{a paBEuMa l1apa-
rrre/rHsM ca laToM xpyxnrl4orr,r 4o6lheuo aanar.
Ba,l'aH je reoverp jcxo reno l{oje jeorpaEnrleEo qltdlEApurlHoM troBpllr[ tr ca IBanapanenEa Il noayaapEa I(pyra.
KpvroBu ce 3oBy ocfoBe Bar6l{a, a aeoqlrr'rnEIpuqHe noBprnu orpaHIlqeH ocHoBaMa 30-
Be ce oMoraq BaJbI(4.
Pacrojalbe Il3Meby ocHoBa Bajbfia je ElrcuHaBar,I{a. flpaBa noja cnaja qeHrpe ocEoBe 30Be
ce oca Baj6r(a. Oa noroNaja oce BaJbI{a npeMa ocltoBll 3aBtlcl ra JIi ieBaJBaX rpaB ll,rtr Koc. AKo ie oca tropMa,r[a fia paBaH oclroBe oEAa leBaJbaK lpaB M heuo [poy'raBarn caMo [paB Barsak'
Ilpan eanex Mo)I(e Facrarll { o6pral6eM npaBoyraoHttfia oKo cBoje
oce ur4 cTpalrnqe
Ha cruqfi 80 npeacraBjLcH je Ba,ltal( Koj[ je lacrao o6pJabeMnoaBoyraoHqKa ABCD oKo rrpaHxuP EC Crla'uua 8S je oca o6pta'6.la crpinriua AD xoja IJB,Jn o]voraq Barbka loBc 'e rlBollduqa.
CrpaH ua AB je rronynpe,ll l{ u' HoBe a rlpaHrue BC AD c!BrctrHe BcLt'xa, 3arxTo?
Uuaaaapuunarioja npt kpera]6y{ aoaripje KpriBy ca
l
IlI
I
I
II
-t-
55
Koa fipBor BaJb(a [MaMo creaehe npeceKe:
a) IlapanenaE fipecel( ca paBE]t ocEoBe Ea cr. 814 (F) Jecle &pyr.
6) Koc npecex npeMa paBfirr ocHoBe Ha crt. 8'l1 (F) jecre en{nca.
B) HopMarHu npece( Ha paBlrll oc[oBe Ea cn. 8la (Q) je npaBoy-raofllII(.
Ci. 79
PaBaH xoja npona3ll Kpo3 ocy BaJ],Ka je clruerpnjcra paBali, a rrpe-ceK pasHr je o.Hr npeceK Barbka. o.H4 npe(cK saLbKa je npaBoylaoHrKayx[He [perrfiii(a ocHoBe x MrptHe - leallaxe BncnHij BaJbI(4.
Konuxo crMerpujcx&x paBlrrl oM:L BaJbaI{?
c
Cr. 80 C,.81
1. UPTAILE BAJITKA
Oprorona,rre npoieruxje npcBor sarbxa qxia je ocroea napa,rennaca xopn3olTanEoM npoje(TlroM paBlrt np[I{a3aHa je Ha cJlnq,t 82 IIouToce rnqpra -r-oca noByqe ce EopManEa oca BaJhKa, a y npBoj flpojekTnojpaBHn bca cuMerpnja ocfioBe napareJlHo ca ,-ocoM. 3artM - fla ocu
56
ce naqpTa Rpyr ca qerTpoM y o" I{oju npeacTaB?ba ocEosv y npaBojBeJIUqrrHr, Taj l(pyr npencTaBJba npoje'( r jy UcJor Barrr{a y xoprrro tair-Hoj fpoje(THoj paBHir r!r, Tj. ry cy ce xpoje(ToBarc o6e ocEoBe x oMo-Taq, Tj. cBe rBBoAHtrqe BaJbr(a, 3alnTo? l,l3Eaa -r-oce y BepTlllta?'rlloj lrpo-
c'e" s' o"je(Trioj paBHlr r,, ocrroBc BaJr,r{a he ceDpojeHToBarr.r y ayxn Be?rnqnHc npeqrllla(pyra, jep cy paBr ooroBe EopManHeHa Brpr Ha,lHy npojP,{r,J) paBatr (,!t).llorxro r-y fi3aoaH re napaJreiHe ca paBHrrr, npojer{roBahe ce y cBojoj npaBoj BeJl'r-qxrrll, r(ao ayxn koje cY ropManne Har-oc). tr41 npB( npojexu jp ,e npoje\ryjyKpajrbe BriArbriBe lBur{e AC I' BD. TnMece Ao6lja qe,ra Apyra npojekqnja Barbr.ay Brly npaBoyraoEnr{a, Ha crttqn cy Ha,r]pTarre jour !Bc r3BonHfirF Barbl(J hojpHl]cJ {pajrhe r on Kojxx je y 4pyroj npo-j.xnrjx j.nHa Bha,t,hBa (P' Q,). a qpyraneBrar'b:rBa (R"S4).
Aa 6rcMo Haqpranlr (ocy clrliry BaJL,-ka rpe6a Ia HaqpraMo Hajnpe ftoclr c", rEyocEoBe-r{pyra, Hayqfirr cMo Aa je l{ocacJrnl{a Kpyra errnca r ofla ce ko}rcTpy-mne kako jc o6ja lreHo y nonraBjby oerrncE. I43BoIHnLIe ce npojaKlyjv cBojoM
[paBoM BeJrIlqruoM Il aoBoJbHo je I,l3 oAroBapajyhr]r Tasaka ernnce noar.rhltfiopMa,re Ea .Jr-ocy r.r Ha cBar(y oa rrr,rx npeHerr{ ayx jeanaky Br.rcllllr.r(Ir3Bonr rqrl) Ba$I(a. Axo cEeee rarrKe crlojuMo, lo6nheMornrdcy Koja npelcTaBJba cnn-Ky roprbe ocEoBe BarbKa. Haj-npe ce olpeae rpaHrrqe BaJb(a,Tj, aBe r.r3BolHnrle BaJbI{a kojecy Eajyaa"Beluje oa rleErpaenmrce o, rj. npaji6e raqKenajBeher DpeqrIIIKa. 3ar M ce,npeMa rorpe6n, Harlpra jonlHeKOJll]KO [3BO]IEtttra ra t]Ilce ral{lle Ha{praila e!'Illflcay fopr6oj ocHoBIl BaJr,Ka. Tpe-6a Boaurll paqyHa o roMeaa ce rBBoaHuqe l{oje ceHe Brrae rlpTajy llcnpeKu-aaHuM nuE jaMa, kao x rle-BItAJhUBt AeO erUDCe y OC-
BE}ItEATI,AL OcHfi IIpeceB BaJbKa
]neroua ']tr.'F,?
s"Cr 83
/ je kEaapar. Kornl(a je
Cn. 82
I
-l-l_I
noJrynperrEulta
4-
57
Ba,nat je nocrao o6prar6eM flpaBoyraoH{(a lyx{ne 3co Il rxn.pllHe 2 cm oko riefoBe MaI6e crpaHlrqe.
a) Xonma je noBptnrEa EeroBol'ocuor npeceRa?
6) Konnxa ie floBprxrua BeroBor napanerHor npeceka?
Bar6ak je [acrao o6pral6eM (€aapara c?paEune 4 cm oKo ocecl.jvcrpuje.
a) KonnKa ie lloBpqrnHa rberoBor ocfior npeceKa?
6) Konuxa je noBprxma rberoBor napaneJinor rlpeceHa?
Haqpraj oproroname Dpoje(qxje lr kocy cJrrr{y BaJbKa nony-npeqHnKa 3 cm, BucnHe 5 cm, Tar{o !a My je ocxoea napa,nenraca paBnx lr1 n yaa,'bena oa H,e l,scm, npII qeMy je a:450
I'2
5, Haqpraj oproronaflHe npojektnje ll (ocy cJrnKy BaJbI{a nonynpeq-HrKa 2,5 cm ij Br]cIIIre 4 cm, TaKo aa My ocHoBa Jrexlr y n1, npx
Iveruy je o-300, q: -2
6. Haqpraj oploroHarrHe npojenqrje npaBot BaJbKa norynpeqF I{a2 cm, BxcxHc 4.5 cm ca ocHosoM ) BcprrKanrroj npojel{THol paBHtr.
2. IIIPEXA I.I IIOBPTUIjHA BAJbKA
Pa rpexeMo ,lr voapi BaJbKa oa (aproHa no rBorH uh AR. nc ranocrenpHu pa3BhjaMo \ paBaH, D06fiheMo npaaoyraoHtll( fi nBd no^.v-
Cn. 84
aapHa (pyr€. ayxrua npaeoyraourka jeIHaKa je o6ruy ocxone ea,rxa,a rrrprxa je jeaHafia Brtc{jllx BaJ6r€, 3Harrlr, MpeNa BaJhI{a ce cacrojtroa aBa noayaaptra xpyra r{ Jeatror trpaBoyraoExxa,
Cr- 85
58
Moaen Ba,bka ir3paalrhelu TaKo lxro helx Eallprart Mpexy Ba]bKa
tla qBprxhfi nanfip, 3ar]rM ie tr3pe3art Ii npaBoyraoHllK 3anellurll yo6rn(y oMorasa BaJbI{a, a ca ropr6e l, aol6e crpaHe 3anentr?tt [3pe3aleocloBc (cfl. 85).
flocMarpajyhx Mpexy BaJb(a BrrrttMo ra je noBplnl{Ha BaJbKa jer_Hara 36npy nonpuuna ocnosa u noBplrrlllle oMoraqa Ba?bka. AKo noBp-lllllny ocHoBe o6erexnMo ca B, norynpe.IEltl( ca r, IIoBp rurty oMoraqaca ,rVI, nncrny ca fI n noBpul]Ey BaJbKa ca P, ofiaa je:
P:28+1A:2nP+2ErHP:2ir (r+H).
3aaarax l. 143pa,ryHarfi noBpLlJl.lHJ Ba?br{a qfija je sficfiHa 2.5cm.noepurrni ocno, npPce(a 7,50 cm".
OcHrl npeccK npaBor BarbKa je rlpaBoyraoHuk qtlja je
Ay)r{uria jenHt,{a npFqHxHy ocHoBe. a LxdpnHa jen-HaKa Bfi('rHll
Ba,o''a, na 2tH.7.50. 1y'3 oBe JenHaKo.rx . -t'10= -t,t.2 2,53Ha,r[ r:1,5 cm.
P:2rr t+m,! 2.3,14. 1,5 (r,5+2,5):9,42 4:37 '64na je
P ^,
37,68 cm'?.
Saaatar. 2, l43paqyEaj noBprrijHy,41:98,81 cm', a BucrHa()6na3all 3a [uBDruuttvJellrakocTn le
narxa qnja je aonpurlna ouorauaH:4,5 cm.
oMorarra je M-2nrH; i3 oBe
M 98.81r - J,52 n H 2.3,14 4,5
r:3,5 cm, na 3aMeHoM y o6pacqy 3a noBplxlrEy ao6]rjaMo
P:2^rU+m= 2 3,14 ' 3,5 (3,5+4,5):21,98 8-175,84
P e 175,84 cm'.
3aAarax 3. I4:eeAu o6pasau €a u3paqyHaBal6e noBprnurre BaJbKa (oa'' Kora je H:2r.
P-2^r (+m-2nr (r+2r)-2't t 3t:6 nt2.
P:6nr'.BEll{6AlLA
1. l43paqyHaj noBpruqlly Barbka aro
l. r-2 cfi, H:4 cm
je aaro:
2. r:2,51cm, H:5 cm
t. r:)! am. n:sian.24:..:aar, n:la*4)
2.
4-
l43pa.ryEarn fioBprxrrHy BaJ]jr{aEnr(y ocHoBc axo ie:
l. r:r.5 cfl. t. r:r!an.4
59
Koa r<ora je BrcIIHa jerriaKa npeq-
,:z! am.4
16era. yrnlrreMo!npa-ocMocTpaEY npE3My,
,q Mprp kyrhje 3a Fa{oBa$e Mcaa Maj} 06,1 d Ba,bKd no,1j npeq-H (a ocHoBe B cfl s cutr" 2 dm. Ko,rrKo je m! ,1 vr nolpe6Ho3a 5000 kyrnja a1{o npll r€paafi nMa 5o/o ornaaaxa?
Konffio je n[Ma norpe6Ho 3a mpary qynKa flpeqEllxa t6 cmayror 2,5 fi?
5. I{yha ayra 20 m x BlrcoKa 14 m rMa aBa_y3ayxHa ony(a o6fitrkanonyEaJbKa I,l ABa BepT{I{aftla Ory(a OOr'I]tKa Bai6I€ llpeqltlll(a16 cm. I{o"!nko je ruua norpc6no aa napary rux o,ryra?
6, IlpaEoyraonuF crpaHuqa 6 cm I'I 4 cm o(pche ce npBo oko cBojeBehe crpairnqe, 3aruM oro cRojc Marbe crpaHuqe, 3a t(ofifixo cepa3nuKyjy DoBprrunc rar{o HacraJllrr rcna?
7. l(caqlar crpan ue 4 cor okpeh. cr npBo oHo cBojp crpaHxuc,3arfiM or{o caMerpajre crpaHrqa- KaKo cc olHocc [oBpunHe ral{oHacTa,Inx BaLafia?
8. KornEo he ce Merapa qvHr{a HanpaBrrr! oA 126 mt ruMa a]{o jenpeqHr{& qyHr(a 12 cm n al{o ce nprnufioM rcpaae ry6u i50/ova.eprja,la?
L Ko"ryha Je floBplxrr d ovoTa!a ea"s'r:r "lja i. B c,Fa jenHat(a
rpocTpyKoM noJrynpcqHlIKy ocHoBe fiaa le noBplluHa oclioBa78,J0.n'e?
10. ll,loqa ,1l{va uMa 06,1rr{ FpaBo)raoH r(d r j( 'J 0rvPHrtjc L57mF 0,80 m. OHa Mo),{i aa .e caer.j. 6r,lo no 0y}l{rd . 6xin norr puI . Ko,1 Ka je ayrx"na no,lynp, 'rH Ha y nlBoM cry'lajy.a r{oJir(a y apyroM?
3. 3AItPElltlHA BAJ'bKA
IleHa je aar npaB Barr,ak (crIII(a 86). AI(o yBr,rJrHy qeTBopoclpaEy npn3My, 3aTr.rM npaBrlJ.rHyyoqaBaMo !a Je pa3Jlnka 3alrpeMllEe Barbl{a ]1 3a-npc!'IfiHe qeTBopocTpaEe npf3Me Beha oa pa3nuftc3arrpeM[He BaJbKa x 3aripeMr re ocMocrpaHe npl€Me.
AI<o v Ba,bal{ vnltrxeMo npaBrjfity nplcMy ca16 c?pana, 32 crpaHe, lxra he 6nrE ca pa3JrlrxoM 3a-npeMnHe Ba,'bka n 3anpeMurre HoBoYn[caEnx pu3Mu?
3axrby.iyjeMo cnerehc: rtrro je 6poj crpanalpaBllrHe npr3Me ynhcaEe y Bajbar( Bch pa3jr,Ixa3anpcMllHc Bafii(a { 3afipcMI'rHe npaBur'Ine Dpr'r3Meje Malra. AI(o 3arreMaprrMo rre3HarHc pa3trrn(e BaJbaI(MoxcMo cMarparn Kao npaBrrJrHy Irprr3My ca Heo-rpaHfiqeno Ber[KuM 6pojeM crpaHa,ina MoxeMo yno-
l
.l
{l1:1
60
Tpe6nTrI tcTrr o6pa3aq 3a r3paqyFasabe 3anper{trie BarL(a, I(ao t 3a3anpeMlrny rlpu3Me) Tj.
V:B ' 11,
KaKo je l{on BaJ6(a ocHoBa r{pyr r,rMaMo
V:ita .H.
3aAarak l.Terna 3a EoMnor IlMa o6nun BaJr,ka npeqBftr(a ocEoBe 16 cm,r Bfic He 20 cm. Ko,lrKo ,1 ,raua r{oMnoTs craHr \ rcrrv?l/ Lr H. KaKo jn 2r. t6 co; ro te r- 8 cn I tiuenoM narur.6pojcea y o6prcrrl u\.{aMo nd jc
y!3, t4. 8I. 20:3,14. 64. 20 :4019,20ye4019,20 cm3.
AKo salrpeMuEy [3pa3nMo y dm3, oHla je
Y!4,0192 dm3.
3aFeMEpnMo J I Ee3rarHy pa3,r[t(y MoxcMo pehn aa y rernyMOXe Aa CraHe 4 [UTpa (OMnOTa.
3aqs'rax 2. Ko,!xl{a je rexllEa 6eroEcKor cty6a 06,rlll€ Bar,ka Brco(orl0 m aKo je npeqH{r( ocrroBe 80 cm, a cnequou.rHa rex{lHa6eroHa 2,5 kg dma?Texfifia Hel(or re,!a ]igparryrnBa ce TaKo lrtTo ce 3anpeMrHaTera roMfiox{u H,eroBoM cneqrlDllqEoM Tex{nHoM
T:V.s? :rr'.H.s.
flperBop[Mo Ar.iMeH3xje y dn, na [MaMo Aa je r:4dm,H: r00 dm
v,-3,t4. 4' . t00:3,14. t6 . 100:314. t6_5024.
T-V . s, T:5024.2,5.TexrEa cry6a je 13650 kg.
E}l{EAE A
L Ko,rlrko ,rrzrapa Boae caApxn je4aa cyg o6,rrxa Ba;br(a quju jerrpeqHuK ocrroBe 4,8 m n ay6[Ea ],96 n?
2. I43pa,ty aj nuBpLxfiHy ,t 3anpevMHy Ba,'r,Ka aKo jr Aaro:
l. r:3 cm, H:3,5 cm. 2. r:2,4 ctt, H:6,5 cm.
s. r:3I dm. a-q! an.243, Ako y jcnaH rlujrrjEAplrqan (Bajbxacr) cya npeqllri(a 0,6 n, AeJrx-
MIIqflo Hafiyrl,etror eolou, 6aquuo KaMcH leoApebeEor o6Jrrra,BuclHa BoIc he ce I]onerlr 3a nora Merpa. Konuxa je aanpeuNla
61
KaMCHa? Ko"'Ifir{a je rexxHa Tor I(aMeHa al{o je lberoBa cfiequ-4u'rra rex{rda 2,3 kg/dm ?
4. Janp.{ Fa jeanor 6a r rr.r 06,1 r{a Ba"bKa je 31401. a Ly6fillr4 m. Ko,tH|( j, rrleqrrrx ro, 6arFrrd?
5. Koi]l1l{o je kg 6a(pa norpe6lro aa cc t€,rlrje 120 000 m xllue npeq-rruEa 4 mn ano je cne(nlDruua rexqna 6atpa s:8,8 kg/dn"?
6. (aa .e y jeaan 6aaett ob,rI4Ha Ba,bKa y,lIje 1570 ,1firapa Bo^e.su"rua hc,e ronprI ra 2Ucm, Ko,r{(n je no,1)np.,rHH'{ 6aJeHa?
7, O(HosHa ueB fiMa yHvrparxHrlr nperlHul{ 18 cm g ae6Jb[Iry 4 cm.HoJaI{o je re[Ko 500 m Te ireBla aKo je cleutltpnqHa rexuDaofloEa s: I1,5 kg/dm3?
8, O! xonuFo kg .nrneuor rBot{ba ce Moxe HanpaBljrtl Bo,IloBoaHarleB ayra 40 m, qfiju je yHyrpaulLu nonynpcrrHul( 34 cm, Ae6ri,{-Ha 3 cm, a creqnon'{da rexrrFa s:7,2 kg/dmr?
9. fBo3aenn o6py.r nMa cnoJr,alxlnu npeqEljx 42 cm, mllpfiHy4 cm u ae6rbnly 8 mm, Xoruna je EeroBa rexnEa al(o je.s:7,9 kg/dm3.
10. Aara je flpaBurEa rpocrpaHa lpu3Ma ocnoBHe nBuqe 6 cm Ir BlI-clrEe l0 cn. Oro r+,e je onncau lr y lt'y ynlcaH npaB BaJbaI{.
L l4spauyuaj floBpurlrHe Ir 3axpeMllHy npu3Me-
2. l,l']pa") Haj noBpLxIHF IJ ranpFMr,rHc o6d Bc,bHa.
3. Oapeln o4roc fioBptrrusa oxtcaHoru vnficaHor Barlxa.
4, Orpetn oalroc 3anpeMnHe onrcaEor Ir yuficarot Ba.6I{a.
ll. Aara je npaEnJrna q€TBopocrpaEa npfi3Ma ocsoBHe uBllqe 4 cmlr Br,rcufie l5 cm, Ofto Ise je cxEcaH n y rby ynncaH Barbal{.
l. l'l3paqyHai noBpurrny u 3anpeMl,rHy npx3Me.
2- l43paqyHaj noBprlrtHe u 3anpeMnHe o6a BaJ!I{a.
3, OapeaH oatroc noBp[rrHa ynucafior r ollucaHor RaIbI(a,
4. Oapean oanoc 3ar]peMrlia ynrrcaHor tt orucasor BaJbI(a.
'12. Aara ja npaBrrrEa uecrocrpafia npr€Ma ocdoBHe nBltqe 6 cm I,r
bH, r. rc 8 crn. OHn tbp je onfiraH r I n,1 je vnrcax ea,r,ar.
1. I&paqynaj nonpullrHy ,r 3alpeutny npx3ue.
2, Vspa,ryr:,aj noRpr[iEe Ir 3axpeMlrHe o6a BaJb(a.
3. Olpeau oqroc fioBprunua ynrrcanor r,r ontcaHor Bri6ra
4. OApeau oaroc ga]IpeMuEa ollucasor lr ynncaEor BarbKa.
62
t3. l{Eaapal crparrlqe 4cm o6phe ce oKo npaBe xoja ie;naparenHaca jeAHoM oa rrlemBux crpalrnla it o! I6e yAaJbeHa 2 cm,a He ceqe (Baapar, I43paqyHaj 3anpeMxa) TaKo nacTa-IOI TCJIA.
14. npaBoyraoBrrx ayxtHe 5 cm u rrinpllEe 3 cm o6phe ce o(olpaBe rcoja ie [apanenHa ca :IberoBoM lrrupnlroM tl oa I6eyAaJbeHa I cmr a He ceqe npaBc*raoHr(. I43paqyHaj 3a[peMlHyTAKO EACTATOT TCJIA.
trl,It(trl
dtrl3l
tII
T.!
x. t{vnAAara je ]rp[Ba m n \aska S BaE paBH[ re I{pIlBe
npaBo p Kpelle \ rroo'ToPy TJKo na . a,lHo lpo,la {q.oll1p].e JaTy Hpxay fl car\{o I len"oJ Ta'lK11, oHna
fipaBa p onl{cyje o6ry noBprr fiojy 3oBeMo koHy.r{arroBprx,
IIpaBa Koja ce xpehe (y 6u,1o koM floroxajy)30Be c- r'BOnHFUa fl ,.Hcpalpqfa, a {o Ba koj)ripaBa Iolrpyje 3oBe ce 
64
I(yne EopMaJrria Ha paBaE ocrioBe oHAa je Ta r{yna npaBa Kyfia, rlllaqeje koca l{yna.Mu heMo npoy,iaBartr cayo npaBy (yny.IInaBa kyna Moxe Racraru 06pratseM jeaHaHoKpaKot rpoyrlla oxo
BIlcuEe roja oAmBapa ocHoBnru, riJrn o6prarbeM npaBoy ]or rpoyrna oxokalefa-
fla cnuqx 90 npeAcraEn,eEa . je xyna xoja je Hacrana o6prarreMnpaBoyrJlor rpoyrna ABC oKo xarere BC. Karera BC je lxcunaKine, xllnorellyara AC je usaonnrqa l{ylle, a Karera ,48 noaynpevnnnocEoBe Ky[e.
Cr.90 Cn. 9l
Hoa [paBe l(yrle nMaMo cneaehe npeceke:
a) IlapanenaH rpecek ca paBH[ ocHoBe je kpyr.6) Kof lpeceK npeMa paBHu ofHoBe Ha je eil-lnca.
B) npecex ca paBHu Koja npora,u Hpo3 ocy Klnc jp ocH{ npe-cel( Kyre (Q' ci. 9l).
Ocnr.r npecer xyne je jeanaxokpaxu rpo-yfao, qIl]II le Kpar( ]eaEar{ ca u3BoaE[qoMr(yfie, a ocHoBnqa ca npeqqnxoM ocrroBe.
Koruxo cuMerpnjc(Ex paBH[ f,Ma r{yfia?
1. UPTATI}E I{YNE
. OproroHa,lHe flpoj.KuHje npcBe kyne qnjale ocHoBa fiapanenfla ca xopt3oHTanrroM paBEg[prraa3aEa je rla cnurlu 92.
lloIrlro ce Haqpra .l-oci, ropualrrro ,ra rlynoByqp ce Bepr KaJHa oca Kyne, a J npBojnpolPr{rHol paBFI oca cftMPTpxJe ocHoBe napa-Jrer'rEa ca -r-ocoM. 3arnM ce fiaqpra Kpyr caueHrpoM J O. xoj npelcraB,'ba npolehu jyocHoBe y npaBoj Be,In'rHHr. Taj xpyr ie npo-
a'ffpTE a'----ri----r-j-_1--
65
iexuria uere nyne' rj. u ocHoBP I o\{oraqa Bpr xyne S npoltTlyjA
'.lJ';;"";; xpi'a (s;)' a cBe rsBoDH,uc J nnrlvnpeuH xe.rora \plra'" ' u ".iL-",it"i
npojexrr'L'rj paBH!4 n'qnRa HV e xoja jc HopMa'rHa
", d' ;;5;;;;"l"ninj p'"i" n1o;"n-b*"n:t ;. j.t,T,l;3i':1it ;l
.r-ocov. H jeanax) "rir"" iO;5.1, jep je or,.unaTaqKe O" HaRece ce [PaBa BertrrxHir
(!ne flaoaJerHa ca pcBIl$ lt Alro cllojxM" tcq'ic S"A' ' S"?"-lYo:"l'"Ii" il""6i"'iii;ii' ;p;jrorr ern'uerx lBo'rrrIJ c Klne hole raJPnHo.a
;;;;;ii.i"; oi'oni nt"ac'au'taj) rl'ol''.uHj) r(]rr' ) qFpr Kar'r"i paBIrI{'
lj#ii.lil, i" au j" 'o j'on'*o*i"*u rpor 'ao rronvnzpan ocrrov nrc'e',v
;;;.'H; ;r";, it r'uorar' ''I aBe urB"4hruc o\4oraua KUlc rr,cy
ul,,i*e v uoioj j. jeaHa y Sxbaj*e, y nojoj je ieana Y
,nbvroi nPojeru{jr erarb na
(pnS'). t lpyra {Q's') He-
BI,IAJ},UBA.
2. (OCA CJlt{l{A
Ha clliiulxoca cjuKa ryre
93 aara jenoll ycJlo-
BoM na jc a-450Iq:'
OctoBa ryne, .Kao vBajr,r{a, je (PYr rI2 Je t(oca
crllHa ocFoBe TaKObe endlrcil
HaqprajMo l{ocy crEKY
{ovfa raKo urTo HaJnpe on-
piit, *o "o"y
c,',I{Y nPerLrlftKar-ocy. AB { CD cY
I
F
iI
f.It-aft-
i"i' "" p,o.oou. *,l,li^"I, j^c*,
"i"i;'i; J"; j" ;" ""Jd; ; ;;;
;;;i; ; ;;";.:; ;.;. 1 :1':" - I'j:;-"?" Jl"ll" ji";';.1;:'1", ; ;X;l*:':ff;;';: "-"'v.'"1'
L"i oaue'"uo oa o
S npencraBJba BPx KYI1e'
Al{o S croj vn ca I{pajfi'x\'{ raul{ava najnl 'rrer lrtpeuxrxa e'tunce
""6'hH; "-;;"' ;;'"-e aJ"jv ,:aoaq 'ra Koie q rrc
'*orrr) n5, rt1,ae rr'
t::ll:;"",;;;", ;; rr"e,r'ovuor trera lpe6a Folur paq)H'r o '-ov-c
li""'"- ir""o"r*" Hoje cP he B Ae I S ui'"ajy ',cnpe'.nrarrH\'1 'lnHrlaMa'
i;" ; ";;;;"'^, a"o e"u' "e ) PaBHx ochoRe'
BE}t{6AIbA1. l4Melryl npeaMere (oji'I nMajy o6'rrx ryrle'
2. ly' rpa'l) Haj a) xuHy |rBollHlluc h) ac ' xja je B c Ha l{) rre 8 cm a
t oLynperntx ocrLOBe o cm'
3. Konnkt'l je npe'rntr xyne 'ula je Jr3Boln{qa l7 cm' a B{caHa 15 cm?
,. nonrnp"ot"* (yne je 10 cm' I'BBonri{ua 13 cfl Ko'rliKa je BtrctHa
xync?
;
i.{rt
lliil
j
I
lo-f
C'. 93
5 reo erlrja M vrii Pa3pen
66
l,lspauynaj noeputny octor npecera nyne luja je tBBoatrqa13cm, a rlpe.rHr'rft ocHoBe 10cm.
L4:pavynaj nonpumry ocHor npece(a kyne qDja je ff3BoaEllqa 5 cm,a BrrcuEa (yne 4 cm.
Haqpraj oproroHa,rHe npojFt{urje I Kory crtrKy Kyne nofl} npe'r-H,lKa 2,5cm x Bxfl,rHc 4.m Taxo Aa je o.HOBa K)ne napaJeJrHaca xop[3o{TaJrHoM npojeKrEoM paBHu Ir oa be yaa"'beEa 2 cm, nplI
,reMv ie a:600 r o: I2
8. Haul''aj oproroH",mc nnojPXU jc r{ocy c,lqK) Kyne noLlynpeq-H Ka 3cm R c He 4,5cm laHo aa loj o.HoBa Je)l{x y \op4']oH'
rarHoj npojexrHoj paBHLr, npa qeMy je a:45o r q: 1
2
3. MPEXA !I TIOBPIIII,IHA I{YIIE
[4oae,1y Klnc, HalpanrbeHo\,t o^ (aproHa, orped vo HajnpP ocHoBJ,rrrv ourjraq npc.ert;vo no jelHol fi3BonHxur pa'BrjaMo ra y IPDHy
paBan. oqfirreaHo je aa oMoraq(yrle
_ npeacraB6a xpy)KIIIl ncerrak,
qllla le nonynpelrHftK leaHaK n3Boa-E!rq[, a ayxuEa rberoBor rryl{a jea-fiaKa obnMy ocrroBe.
fpa(PuqKri Mox(eMo npu6rrx(rloaa EaLIpraMo Mpelky ky[e. Tpe6anpBo [aqpTaT[ r(pyr ocHoBe ri [oae-?'rrrrr ra Ha [3BecTafl bpol IIenoBa.(YKonliKo je Behr 6poj MaH,rIx !e-roBa yrorrx(o le ra.rnocr neha.) IIpo-lyxnMo Jeaas npeqrru( Il oI l{py-xEnIIe HaHCC,'MO Berl,lqfiEy U3BOA-slr{e s. TnMe cMo olpeIrjrn qeHrap(S) oror kpyra, 'rrjr je rrce'rar oMo-rarr Ryrle. HaqprajMo rryH ro,ryxpeq-HtrI€ s It ]ia Eera lpeHecllMo Ter!]BeI{pym y ocnoBnJ oHonn(o nyTa r(o-JIIII(O TLiX ACJIOBA
'{MA.Kaa cc (pajeBu cxoje ca qerrrpoM S, ro6rda ce oMolarr Koj{ rMao6rnl{ (pyl{Eor [ce'I(a,
n,),fi H\ ,rlhd ovoraqa Hync vor{eMo raqrro oDpe[ Tk pacvtloM.ar(o 3Ha o qeHtpaLlHr,l vlao a (c'rr. 94).
O6xM (pyra ocHoBe (yne je O:2ar. I,lcro roaul{a je ',
.qyxlrlraJ,ryka l(pyxnor rceqka, qlllll le fionynpeqllli& 5, a qeltrpanHn yfao d' Tl.
znr- " -s^ " , 113 oB^ pe,lartrje ce voxe v3pa'ryHarI uprrrpaJrhr] ] ra('
1800nocMa IpaHor qceq'{a. Tj.
o: t 360".
-s
5.
6.
7.
Ci. 94
hI
ocHoBe r Il u3Boal lqa s, Mo-oMoTaqa I(yne a xoHcTpyncaT{
AIro cy IIaM no3narn rroJrynpeqHnnxeMo yBer{ u3paqyHaTu qer pafilr' yraoMpexy.
Heka je r-1,5 cm, s:4,5 cmjonaa je
": -!.-5- . aoo": 1.366': 12s0.4,5 3
143 Taq(e S (oHcrpvtrIIuMo nvR nori-npeqEur{a 4,5 c , Il otpelrrMo qeE- A'rpanHn ymo 0..1200. IZ3 laqKe SnoByqlMo 6trno rojY noryrpaBY xojahe ceh! nyH AB y BeKoj ra-rKr-r C,na Ha rny HaHe.rfMo nyrl{ /:l,bcfl..Ilo6ftheMo uenrap (pyra ocHoBe B,KOj,l he noAupJrBaTfi oMoraq.
Ora <fnrypa flpeacraBrba MpelnyoapebeHe r(y[e.
flocMarpajyhn Mpexy xyne ao-rra3[Mo Io 3ar{Jbyqna aa Je noBptlrnHeKyfie jeAEaKa 36upy roBplxnra ocEoBe fiyre lr oMoraqa-
AEo noBprnnsy oNrorarra o6er'rexuMo ca ,r!l, noBplllffiy ocEoBe ca Br noBpur Hy l{)n( ca P oHAa.e Mo)l{e Han .ar na je
P:B+M.
l_IoBpuuEa ocHoBe je npyr Iorynpevnuxa r, ti. B:ne.lloBpurra oMoraqa. Kp) r{Hor ce"Ka, jeaHar{a jP noJynpor3Bo4y
.qyxxlre xpyxHor r'ryi<a 'I
llonynpeqHnEa
Kako je aynanHa r{pyxfor ryra jeaHana o6uMy l(pyra y oclloBlr, rj.2'!r. a no,r) nfe'rr K ip jcnHaH 3Bodttrur't s. ro,"lenr Da j"
n:L'znr's rnr M:trs.a
Yl(ynfia noBprxuHa (ylle jep:4f2+nrs n vP:,tr(r+s).
I43 oBor o6pacqa MoxeMo r3pa3l,rrIl noBplnrsy l{yne qnjn ie ocEnnpece( jearraKocrparrnqH[ lpoyrao, rj. s-2r. Taaa je
P:nr (r+2r\ tuttl P:nr '3rP:3 rr2.
3ararax l. IIpaBoyM[ rpoyrao vaje cy l{arere 4cm r 3cm o6phe ceor{o ayxe r{arere- I-,l3pa.ryHarlt noBplllnEy TaI(o EacTaJIe Kyne.
Cn. 95
68
I4saoAauqa (s) oBe kyfle je xunoreny:a npaBoyr.nor rpoyrna, aMar6a karera je no,r;npernux r-3cm.
,(yxuny rcnoAuurle rBpa,ryEaheMo npnrenou lluraropr.rnor fipaBlrrra-
s!:t+H!:J!+4,:9+ l6:2b, s:S cm.
IlpeMa roMe je
P:rr (r+s) ! 3,14.3 (3+5):9,42.8P -75.36 cm'.
3alarax 2. noenara je B fllHa xyne H 14ctj u x3so4Hnua s-26cm-I43paqyfiar! besy noBpurrrHy.
,[a 6[cMo u3pa.ryflar( noBprxltny kyne MopaMo oApeArrn AyxnHynorynpeqErlta r. 143 npaBoyrror rpoyrna, IlprlMeEoM llm4ropnror npa-BfiJIa, rpe6a oApeAr.rT[ xaTeTy r, r(aAa je no3Hara xlrioTeHy&l s ti !pyr&ka rera H, rj.
f:s2- 11':26' -242:(26,24) (26+24):2.50: 100, r:10.IIpeMa roMe je P::rr (r + s)
^, 3, 14 . 10 ( l0 + 26):31,4 . 36
Pr 1130,40 cm,.
BE}I(DAIbAl. Hallpraj Mpexy (yfie noryfipeqlrlrt(a r:6cm n [3BoAH[qe
s:gcm, a 3arnM r.BpasyEaj noBplrnHy Kyrle.
2. Haqpraj Mpexy yrle qrju je qeErpanH{ yrao 1200, a tronyllpeq-HIlr{ ocHoBe 3cm. KoJrrka je noBpnluEa oMoraqa l(yne? KoJiuKaje noepuuua xyne?
3. Haupraj Mpexy kyne 'rrjr je npe.rHnk ocnoBe 6cn1,.3
ocHotse jeAgal(a ca-: noBplll re oMora.Ia. Ho,]rlt(a je
KoJiuKn je qeETpardr.r yrao?
a [oBp IlEa
n3BOIrillqal
4, flpaBoyrnn rpoyrao qfije cy Karere 12 ctrr u 5 cm, o6phe ce npBcol{o MaM 3aruM oxo Behe karere.
1. l43pa.ryHaj noBptrrfiHe rar{o EacraJrrrx Ky[a y o6a cnyqaja.
2. Xafio ce oAnoce floBprurlHe r,uxosrix ouoraqa?
3- 3a Eo,lnko ce pa3nnKyjy rbnxoBe IloBprxufie?
5. Koauru je yrao KpJ )r{Hor n.eqka HacraJror pa38rjar6eM oMora,raI(yrle qfiju je o6uM ocloBe 6,28cm, a n3BoAHuqa 5ctn?
6. XonltKa je rroBprruEa oMorarra xylle, quja je rBBoAHlqa 6,5cm,a o6rM ocEoBe l2.56cm?
69
7. Xonrrlca je noBp[rmra oMoraqa rryrre quja je ocsoernqa 21dm,
a nonyfipeqHfiK ocHoBe 21dm? KorIrKa je rloBplIruEa l(yrle?
Kako jc :arneraHa ua,bKa I -BH ro je :anl,cMlrra r') ne /. ] BH.
AHo .a r o6e.nex \ro no,r)rfe'rH h o.roBe MaMo na k V- I trt,H.
3aAara( 1. Hoauxa je sanpeuaua Kyrre) fioJrynpeqsu(a ocHoBe 6cm nBrcuHe l0 cm?
v- ,!r r, u: 1 .:,ta . 6, . ro :V:376,8 cm".
1 . :t,+.:6:e,,a.tz:szo,a.
8, Haqpraj Ir rBpa.ryHaj noBpllrmiy oMoraqa oHe kyue qlrja je x3-
ocEoBe 24 cn, a
.rr-rja je ocHo-Honrka je noBp-
9.
10.
3. 3AIIPEMIIHA I{YIIE
Bfiae,]lr cMo !a je 3anpeMxHa Ba,Bka lbyriKqr-ija noBpr[]rEe ocloBe n Mep-Hor 6poja B crHc. ynopehxBaH'cv ranpeMHHe aa,'rra I :anpevrne xyne 1el-Haft xocrroBanlpAHal{ \ BrcxHa HlBeruheMo oopa3au 3a 3anpevuHy k\nF,
3a raj orfie! y3MeMo Moaen l(yre rr MoAeJ! Barb(a xoju uuajy jeaiaxeocEoBe Ir JeallaKe B,lct{re.Moae"rt sa,rbxa x rryrre cyrnyrj},u,
HanyHr.rMo More,r ky-IIe BoAoM aJrn ofinuM ne-cHoM fia ra flpecnrrMo yBaJbax, Bu4eheMo jla he ceBarbalt fianyHnTr{ ao tspxaTex ,fiocne rpeher npccx-
. To EaM nor(a3yje aaJe 3axpeMr.rEa r{yrle TpunyTa Mar6a oa 3anpeMlHeBaJLKa ca EojuM uMa jcA-Har{y o(:HoBy ll BticllHy,
BOAIIUqa locfii, a BIIcnEa 6cm.
Korurxa je noepuuua Kyne qrj{ je fipeqnruBucbad 5 cm?
Ocrrx npeceK xJ ne je je!Ha(oKpakI tpoyraoBuIa 4rm a no€purrHa o.fior rpcceFa 3.ms,rrlufia kyne?
tl. noBplrlufia oMoraqa kyne ie 28,26 cm2. Konnxa je notpunra nyneaKo je ayxrHa norynpevnuxa 2,5 im?
-- - --T -----
v0
3aaqra( 2. Konst(a je BrlcriFa r<vae oa anyMnl ljyMa lloryfipeqExKa oclto-Be l2cm lr re}irufie 17,804 kg, aKo je crlertll(blrqHa re}l{lrEaanyMnr{rjy a 2,7 k9ld10t'?
143 o6pacua 3a rexfirry I l/.s no6rjauo aa je:
y: T :!4!:6.5sa.
l|J ofupacua 3a x3lcqyHaBabe sanfeM Hc cnenx !a je:
' nf.H-V. KaKo ie y -6,594dmE xMar'ao ft je3
'.3,14.t2!f/=65943
| .:.r4 . r+t ft = 659+3
,- 6594 = q1.75. ri. fi+43,75co,, 114.48
BE}l{1.
2.
BAII,AKontrxa je 3anpeMtEa Kynea Brcrsa 0,5dm?
l(onijl{a ie 3alpeMnna ryne12cm?
3. I43BoaHlqa ryae je 2,5cm, a Bucrua 1,5cm. I'l:pauylaj noep_rnllHy r.r 3anpeMtHy l(y[e,
4. flracr ceHa IrMa o6n]rK Kyne qxjt je o6uM ocHoBe 12,56m, a B]r-cgHa 6m, I{o,rIII(a je 3anpeMllHa rora n,racra?
IloBplnlrlra oclor fipecera xyne ic 17,5cm'. I{onnKa je noBplllffiar sanpeuuna lryne aKo je [oJIyrIpeqEr]K ocHoBe 3,5cm?
O6uM ocHoBe je 12,56cm, a [3BoaHr'rqa Eyne je scm. Kontra je3anpeM[Ea Te Eyne?
7, floBpunHa ocHoBe (yne ie 50,24cm2, a Bltcl-iHa je 3cm. trbpa-qyHaj noBporxHy r{ "anpev{Hy
K}ne.
8. I43paqy[aj noJ]ynpeqEuK ocHoBe sllja je tl3Boasltqa 6cm, a qeH_
TpaJrHn ymo Kpy)I(Eor lrceql(a 1200; 3arl'lM IBpaqysal IIoBpnIuIryIl 3anpeMffiy re Kyne,
9. floBprxriEa xyne je 78,5cm'. Holuxa je 3aDpeMIrHa al(o je En-cr,rHa lryne 8 cm?
lrjr ie norynpeuurx ocHoBe 2,5c!l,
qnja je rl3BoIlrrqa l3cm, a BucnEa
6_
7t
10. I43paqyHaj [oBp[LIHy I{yflelJt4 4d.m.
It. Ko,lrrKfi je no,lynpcqHa( ocHoBe npaBe xytre q',ja je JarpeM4fla314cfl3. a Bxr'tHt l2cm?
lZ JenHaKoKoaHr roaner qxie cv o, HoBxue a-26cn, b-10rrn, a
HpaK a-l7cm b6pl'. cn ono e"he ocHoBr'lqe. l4spa'{yEaj noBp-niuny r aanpeurny raxo nacra.nor'iela. . l .
13. JeqfiaKo(paKn rpaflei qfije cy ocrlosBtlc a' 40cm, b--30co, axpax c-tjcm o6phe ee oxo a) Behe 6) Matt'e ocroBnqe l43p&qyHaj [oBprraEy Ir 3anpeMffty ral(o Hacfarrllx rejla;
,
14. JeanaHocrpaH[qH[ lpoyrao crpal qe a o6phe ce oRo cBdje Bi_crEe. 1'l3pa3[ rloBpu[Ey ]l 3anpeMllHy ralro lacraror reta Kaorhvnxqlrjy crpauuqe a.
t5. PoM6 ABCD crpaHrue d-4cm u J r,la A -600 96ph. !!,1*onpaBe Koja npo,ra3r Kpor raqKy A n HopMairHa le Ha aHjaro-Hary CA.
a) I&paqyHaj noBpllrllny raKo Hacraror reJa.
6.) l43pacyHaj 3aflpeM Iry raxo HacrarlorTeia.
XI.J'IOnTAC$epu noepm lacraje o6prarbeM nor'ryl{pyxHxqe oKo cBor npeqHxl{a-Ceaxa . r"xo cninha qogputl rorj' r'a(o j" )n..,cHr on iplHc
cTan8e Tirrrl{e qerrrpa cocpe, 3aulro?
"rlonra je r.eoMerpHjcko reto orpanxqeHo c{epnoM noBplxx. Ta noBp]lI
je kprBa, iep Eacraje o6praBeM (puBe Jrr.rHrrje, na je aonra {)6110 reoMe-rprljcr{o rerro. ,rlvri xoja cnaja Ma kojy raq(y clFepHe DoBplnlr ca rIeH-TpoM 3OBe Ce no,rynpeqHrr{ jronie.
Cr. 97 Cn 98
Aro .ron r rpero"- o Jpo o! frBrr. Ho a po.ra. ip,, rH iJr.npecek je fipyr. xo"rrynpetrHnna jenna(or norynpeqHlrr{y JroITe u Ha3uRace Ber''rrkx ripyr !'ronre (cru(a 98 npeqnujr AB).
flp..'x no I' ,r plsH, Hoja ,r' np ''ra .{por urHrap ronrF e(pyr, u Ha3nBa cc Manx ripyr r-ronre (cruKa 98 npeqHHK CD). Rpyr jeyTojrrrr{o Marrr yKoJrLKo je Brrl]e yae.rbeH oa qeHTpe ,rronre- 3a ro?
1. IIPTATbE "IIOIITE
Opror'onarue npojeKuuje ronre npr(a3afle cy Ha crnuu 99.,rlonra ce npojenryjc y xopr'r3oErarrHoj r BeprnranHoi npoje(rHoj paBIrn
cBoj,v BPr.H \r rl\roB. va. r'jr,r.Y rFrrpr' r.poj-nLl]P 'eHrilpd ,loflrF
II
E.
na 6xcMo olpenfi,rfi jor! H.Ke ragKe Ha Jlonrfi DpeccutjMo je paB-Hl{Ma KOjC C] nzpaieJHe ca n1 (oHna jc rsfiroB noio)l(aj HopMaiaH ca E2),Ilpeceuu ca JronroM c\ (pyroBn xojx ce y paBHH fir npojekryly y cBolojnpaBoj BenrqnHu (I'2') tl Q' a'\ a y n,, npojeKryjy ce xao rerriBe (1" 2')6 (3" 4" ).
flpeceqrMo nofiTy jeanoM paBHLr koja npona3lt fipo3 qeETap, Eop-Manna je ca r!1, a ca Bepr[r(anHoM npoje(rHoM paBlill (EJ 3aRnana lleKx yrao.
t'ztl i \>r
/L,l' t\j)
utls tl
ll lN r-4
OHa he ce y xoprBoHrarEoj rlpoje(-rHoj paBHr npojeKroBaru fiao npaBa Kojarrpona3 Hpo3 S' x ceqe BerxfiH Kpyr yA'B', a uame t(pvroBe y C' D' u E' F'.
Jlaxo oapebyjeMo raq(e y kojl-tMapaBan ceqe Mane KpyroBe y ne, noafir-neMo HopMa?rre Ha, ,r-ocy ao npecexa caTeTUBaMa, Tl. fipoiel{qlr]aMa Marux kpy-roBa y fi2. AKo _Te raqxe cllojnMo_flyxo-BriMa y apyroJ npolekqulfi aoor]aMoe?rlrncy_
Kocy rlvv5 ,non re uprarseu nrjeral{o ri3Becrrr, a n qprex He 611 6uo oqn-
o1
Ci. 100
r,1eraH. 3aao aJ 6rcMo darrpr,r,r, nonr) loBor'rro je !a rrvrl.r/\In lro-6y. ,r{ }yxcaH rloaP,r ronle rhPrc npa!.1aBLivo c,lHHo11. llaupldMojiaan xpr r (xojl 6I np,'. r, ,, HpoJ no,'loBe l'). Ja Iv jc!iH (ol14 lrpc4-craBr6a er(Barop (4) u jcaaH ep{auiaH (fi). KpyroBe 4 t,l m llprarlo Eaor{occ cJlnKe xpyroBa, rl l{ao eilfncc,
Ha c,lfiqu 100 ryxa SA, SB, SD cy nonynpe'rHnufi ronre
2. NOBPIIII'HA ,IOIITE
I{axo aofirnHy l]oBprrr Hc MoxeMo pa3BLTlr ]r paBall, To treMo ce 3a
n3Bobe}ne o6pac{a 3a n3paqyHaBalbe noBprx[He fiocnyrr{nrl, oBr{M otJleaoM.
!I
,,v I
,,' L,-
74
3al{aquMo jeAau KPajIIA)I''bI'BO IiAMOTABAMO IlOrroT yEo lroxpEje Kao lxlo
y3MiMo oaer apBeHe Jlonre kojlr je noaeJ6eH",la [Be fionyjlonre' triBIBI
I{allafla y tlajBl'Illy TaIrKy fionylonTe, Ira fanoLlv'lo frlHol noBllu l2KO [a joj cP noBptu
1e riprxarano Ha c"r nx l0l.
Ilocre rora 3al€quMo Kalrafi y a\eHTap nory_,llonre tra ra [aMoraBaMo cBe aox Ile IloKpljeMo no_
a.Bp n Kpyra.yfiopebvjyhfi l(aHaII rojlrM cMo rioKpItJII'r roBpu
fiorrvnofiTe ca KallaIIoM Koj{M CMO nOKptJIr fioBpmHpyia. Bxr tro aa j. dyx Ha r(aHana KoifiM cMo
npi'npu,r noapu, noi)ionre aBa n)Ta sehd o'0 (a-
"lnu'nnl"" "io np.xpn,ll noBpLx Hpvls Kcxo tto'rryqll"e an'e nory"onie, 3Iraqll aa EaM je [orpe6EoqeruDu nvra BuLxp HaHana aa b4cllo np.l{1,r"'lr noBplx
,un'i'' nd tto HaM je norpp6Ho aa 6rcuo rrpexpr'n'lnoBplrl BertlKor r(PYm.Cn. 101
Ha ocloBv rora ral{JbyqyieMo na jc noBptlluHa Jonre qerrp4 nyra
o"l,u on nouoJun. Be,lltKoi lilvra Oryfla je o6lcJau 3l ]t3Pc l) Hamrhe
roBpunHe rl6nre:
' P:4nr''
3aaarax l. l'l3paqyaaj rloBpn]I,llry nol1Te qrjlr je nofiynpeqHrB 6'25dm
P-21tla.' 4'3,14'A,25'?:4 ' 3,14 39,0625: t56,25 3't4
P^'490,625 dn!
3aaatar( 2. H3paqyHaj ayxuEy norlyIrpellHn!{a ronrc ruja je noBpUII'IHa
12,56dm2.
P1y'3 o6pacua P 4ir2 r3rtar la f (2
4n' a
eroM noBprxuHe y o6pacqy ao6ujaMo:':1l* ; 3a-
,: !!!ft r,r:r, ri. r:rdm,
3. 3AIIPE]VII'HA JIOITTE
Aa 6rcuo aouarl ao o6pacqa 3a IrcpaqynaBabe 3anpeull e rorrenocrvxlheMo ca ieaH{M orneaoM.''''3;;;i
or,len nav i. nolte6a' voner u)rlrbe nu'lyilonre I Moaerl
txvnroe xyn" urja je Bl,tixH3 jelllaHa norynp'qH Hv oclloBe r(ol14 ]rjeAflal( ronYnPe'IHr'II(Y "ronre.
HanyruMo Moren (yIIe BoIloM na ra flperl]jMo y no'lyJonry -Buae_heiro qa fie ce lroJryronia anyHrlTn ao Epxa rel{ locre apyror npecu-
nar6a. oBaj or,reaBeha oI 3anpeMllHeBeha oA 3dnpeMuHe
.
noHa3yjc aa je 3a[peMuHaxyne. flPeMa roMe, 3aripeMrillaryne.
75
noJrynonTe aBa rylaroflle je rieTfipx nyTa
Cr. 102
Kaxo je 3anpeMllHa kyne
$,.H.
TO je 3allpeMxlra noaTell
V- ,tP H;3
no lo je xoA tonle H:r Ir aMo Aa je
4V: ^
ta'3
3alara( 1. MaJu norlrus Kpyr nonynpeqxr(a r1:3cm, yaa"'hen je rl4qeHTpa rronre 4cm. Koffrfia je noBp_
flprMeEoM l]l{raropltHor npa-Btrra (crfika 103) rcJa3fi aa je
f' :42 +3' : t6 +g - 25
r:'crn, P:4nr'-4 3,14. 25::3,14. 100
P=3l4cm'
3aAara* 2. l43pa.IyHaj 3anpeMEHy nonre qltja
P:4nrA Y: 4 nr":4 ng: !-333
4nra:324n/2:8lr:9cm. V:g72icm'.
v:)3
Cr- 103
je roBprxnHa 324ncm'.
n7 29:4.n. 243
76
l8E}t{6At6A
2-
t.
7.
aBo je:
3r: -m.4
4.
Haqpraj oproroEanEe trpojekrr&je nonre noryllpeqllllKa 2cm,aKo JrolTa aoarrpyje o6e npoje(TEe paBH[.
Haqpra, oproroHanne npojeKqnje ronre rrorynpeqH[xa 2,5cm,ano ,onTa troalpyje BepTtraansy [pojeKTHy paBan, a oa xopr-3OsTaJrHe npojeKTHe paBElr je yaaibeHa 2cm.
06rr,r npecexa ,lonre je 18,84cm. Ko,t'lk'r je nonyflp€'tHrrK nonreal(o je np;ce( JlorITe yAaJberl o,4 qerrrpa &cm?
IlonynpeqH[( npeceKa rotrre je 5cm, Ko,Tlrk[ je npeceK yta,besoA qeHTpa noflre noryfpeqEfi(a l3cm?
5. Il3pasyHaj noBprnIrlly & 3alpeMrEy rofiTe
a) r-ldm, 6) r:2,'crn, B) r:0,5m,
6. I43paqysaj noBprrrfHy lr 3anpeMrrHy rrofre aKo je Aar o6IrM Be-Jrxr{or (pyra:
a) O:12,56cn, 6) 0:9,42, B) O: I,57rn
8.
l43paqyHaj noBprxrrEy rl 3anpeMuny Jrorrre aI(o Je Aara floBpuluEaBenrrkor llpyra:
a) P-253,86cm', 6) P:7B,5dn', B) P:19,625m'
l43paqyHaj 3anpeMnHy norrre ar{o je rara roBprlIIIIla Jronre:
a) P:3l4crn,, 6) p -28,26ca2, B) P:78,5drn'.
KonfiI{o je rclnl(a (yrra rlonyrlpeqHlll{a 15mfi oA:
a) onoBa, axo je s:ll,4skg/dn'6) nnarane, ako je s:21,45g/ca'B) 3nara ako je s:19,36e/cm.r) 6anpa, ako je s:8,8g/cm,?
nonynpeqEIII{ 3eMrLe je 6371kn, a fio,rytpe.rfi[K Mece{a l738km.
a) l{aHo cc olllloce rnrxoBe noBpnlfine?
6) Harro ce oanoce rtuxoBe 3anpeMrlne?
ll. Ko,rrr{o.. Moxe u3Jthll] r{\tiuua nppqHrHa6aKpa 'r ja j. cneu On'rHa iexrra 8.tikg dm'?
l2mm oA 17,6 kg
r0.
12. Oxo npaBoyr',ror napanenenaneAa qrje cy AriMercrje 3cm, 4cnl2(m on caHa je ,1orra. h.!paqyHal noBpur Hy r,r ranpeMrHy
J
I
F{j'
l
13.
l4-
7T
y roqKri uBlqe 11 vnrcaEa je r or{o be onucafia roflra.
a) OapearI olEoc noBprrrfHa ,onr[.6) Oapear oanoc r*vxoBux 3anpeMuxa.
Ilpeceqr'uo Jronry flonynpeqHlr(a locm jeAHoM paBHu Koja jeHopMarHa Ha cpeALHy jeAfior loJryrpeqHur€,
a) l43pa,ryEaj ronynperrHux npeceKa.
6) l,l3paqyraj noBprnlHy xyDe xoja xao ocHoBy r.rMa npecer,a q,Ij]' je Bpx qenrap nonre.
B) l43paq)Haj lanpeMllfiy rp Kync.
r) KaKo ce onHoce 3allpeMrHa xylle u 3a[peMnHa Jrollre?
lllynJba ,rofiTa oa 6a(pa rua cflorbaErr6r: npeqHr( 36cm, a Ie6-JblHy Bcm. Xonnxa je rex{rrla re Jronrc ar{o je s:8,skgdrn3?
fllynJl,a .renuqEa nonra nMa yHyrpaurbr npeqHr{x l6cm lr ae6-.trllBy 2cm. Xonuxa je rer{nEa aKo je s:7,8g/cm3?
Jeaan craKneEr-i cya uMa o6nuK nonynonrc qnjn le o6rM rop6eocHoEe 62,8cm. Korlrfia je 3anpeMrHa ror craxaeuor cyaa?
Aro ce oa apBerre (oql(e ItBurle l0cm ficrelxe HajBeha nonra,fionurro npoqenara n3noce oTnaqx?
19, V npaeaaau rerpaeaap lBurre d vnucaHa je I' ol(o liera orucaHaroIlTa.
a) l43pa'ryHaj
6) 3a l{onfixo ce pa3nr(yjy noBprrnEe re aBe .rorre?
B) Kofirl(o fiym je Beha 3anpeMrrla onrrcaHe !'ronre oa 3a[peM'lHe.y[ucaHe r'IonTe?
15.
16.
17.
r8.
:
t
nor\ nneqHxH vnxcaHc I IloJrvDDeqH k onxcaHe
flpecel( lrJlr npotbun cBaKorI(oje quHe 3aTBopeHy. t3JloMl'beHy{oHrypy. Kolrrype tpeaMera cy
XII. CJIOXEHA TE,'IA I'I3 NPA(CE
l. IIPOoI'IJI TEJIA, l{OTIlPAtt'E It AI4MEH3IIOHIIPAE'E
CRopo Ha cBaKoM r{opaKy ce cycpeheMo ca p'"nuY -19-"1Y,:1:Y9
xoja cy iacraBJL,eHrr x3 lBa ut'Ift Blllre HaMa fio3lurltx reoMe,rpl,rjcl(!'{x
'reJa. fal(Ba TeJIa Ha3trBa o cJIoxeExM TenlMa
llnTaH,e croxcHol reia Ha Haq H ca l(ojru cvo ce ynolHanl'r'qe.ro iir uo,lo TeulKo 14 Hxie o'l rnr[flo na re cJy]l{r'lMo HoBx,{ Haq HoM
;;;-;;";;, 1or re,ra rroioh) paBHor nPP'eKa Ta'.aB HaqnH npYKa3x-
Baf6a reJla 3oBe ce apo$tlnupahe.Tera Ha qprexy je orpanu'Iell trBlqaMar-rru xpt{By nlrHujy, onHo,cHo rheroByB A"bLjBC t UpTaMO t{X Aeljenlt rtrBl',l-
jaMa, a fieBxa,'I'rrBe naHUle flcnpeKI{-
AAHUM.
KaKo Bchr'rHa npeaMera xlla rIPa-
BrJraH o6JIIrt{ cxMeTp[rlaH y oalrocyHa rel{v 3aM[LllrbeBy ocy. To lt ]$lrx
upTano nlult{joM ufra T:lqKa. PacTo-j;t6€ 3Meby rlBe raqkc,,I'rJltl PaBaHna upTexy (,6e,lcxaBarro OPoleM olllce :ose xora, y6e,lexaBathe bpolcBa
Ha qprexy noMohy MepFrx nnfiujaje ftornpat6e.
Tpe6a Boalrrfi Paqysa aa je6poi ]BcR na cp.arrl{t'r Meplte JIirH jeKore u3oaxaBaMo YtseK rclxM MeP-
HnM jca;lnlraMa, 06rl'110 y MllJtrrMe-
TDIi a. aJII'l ce o3HAAa ,,t]fi" He craB_
,o'r. Ano ay Mele Aare Y LlexuM aPY-
rrM icalrutqaMa, Y 3aaarKy ce roopa HarJIacuT .
Ha c r ltx l0i .\ 4ara aBa oElJ {{Td nptautta ai cy rh{xoBtr
"p*.r, np"o"t""*"ir ucrov xonrypou rj npo(!!a'1 cj r'1N lr aHak
oR. ^8, oarr qrra npeave,a yJ cn crBarbe oapeh'firlx o3Ha(a
""' ' ;.* ,;;; '""rrr*o". ',.' Aa 6M " cc laBHe noBpt, 6o'bc Mcra'.rc
;,;;,,,;. ;y loLir r oe"va s jarorraraMa rB) qcHxM laHHfv nnHrjava
il;;;;"p'.;",-" uu,rvsaorqnr'x noBplxx o6errPn{aBajy cc r{ora\'t' x' npPtr
r{oir4x ce fana3x 3BaK o.
Cr. l0l
7S
Ilpo{bxJl jealror nperMera aaror qprex{oM: oMoryha Ba aa ce tBpaqy-najy IneroBe anMeH3ffje, Da ce ro Ha3nBa af,MeE3{ofinpaEe.
3aaarax 1. lZ3paqyHaj 3anpeMuHy flpeaMera nptlra3alot rlpo(brnoM Hacnru 104a.
OrHake flopel Kora Ha{a noKasyj} aa je npcAver cac-TaBJbeH l'3 rBa Bar,Ka, na je yxy[Ha 3anpeMuHa:
V:Vr+V. r trpeMa roue
v:v\'H,+B'H,B=nr?.H.+nr4.H,
V - 3,14 (12,5' 10+5' 25)
V - 3,14 (t562,5 +425)
V * 3,14. 2t87 ,5
7 a, 6868,750 mn'.
3aaarar. 2- I43paqyHaj roBprrllHy npeAMera npulG3aEor Ha crllr{n 1046.npeaMer ce cacroj! u3 npaBoytJlor napajleJle[ttreaa IrBaJr,r{a. Kako je ocHoBa BaJbxa y paBHt npaBoyrnor napa_r'IerIeDIl[eAa, TO [OBpUI'rsa npelMeTa
P:P'+nrae Pr npeacraBjba yKylEy noBplnlllry flpaBoyrncr napane-renMncfla, a M npJAcrcBJba oMolaq BaJbKa
p : z - 25, +4. 25. 10 + 2. 3,14. 5 25: 2. 625+ 1000+3 1,4 25
P:1250+ 1000+785
P-3035nln'.L,l3pa'rynaBar6e 3afipeMltfle cJloxeE]tx reJla y fipaKc], cc ynpoilhyje
jep np{6nllr({r pe3ynrarx npaKrl{qku 3aaoBoJbaBajy.
. C'. 105
3a r8parryrraBaH,c ny6arype apBera
E\!\
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flocroje npn6ruNnlr o6Pacqlr(cra6ta) Ir 3anpeMlHe 6ypera.
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O6pa3a[ 3a npr6nl'rrEo u]paqyEaBar6e HeorecaHor cra6na je
v- -r- . c.. n,21t
rAe je C o6rM cpe,qrger Dpeceka, a H Bllcv.c.a cra6ta.
Cn. 107
O6pa3aq 3a 3anpeMuEy orecaEorcra6ra .rlrjr cy nonperrHr npecequ kBa-aparu je
IV: C2 H.
25tc
rae je C o6uM r{pyxHnqe onxcaEe or(ocpeArier npecenaj a lI Bnc{Ea apBera.
flocrojr xrue o6pa3aqa 3a r3paqy-HaBabe 3anpeMrHe 6Jpera, Jeaan seoMajeqaocraBaH T3B, f rMeHoB o6pa3au je
rAe je D EajBehn flpeqHr.r(a H BxcuEa 6ypera.
v:0,82. D. d. H,
6ypera, unlr ,Tp6yxa", d je npeqr rk aHa,
BE'{DA}bA
l. Vspauyvaj Texuey onoBror npeaMeraje npecex npriaaan sa c,rlrllu 108,3a 500 roMaAa oBaKBrx [peaMeTa?
ayror 20cm (s:11,3) qrjrXonfil(o je onoBa Ilorpe6go
Ci 108 Cr- 109
2. l4spauynaj noBpruuay l 3a[peMlny npeaMera np[Ka3aHor HacJurqn 109.
3. l43paqyHaj 3anpeMHFy uyne qrj je noDpeqE{ npeceK npuKa3a}tEa cnurlu 110 axo je Irefia ayxrEa 4m.
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larruraeEor oa MepMepaI43paqyHaj noBputxHy rexHll] TeJra(s:2,7) np6Ka3aHor Ha cJrfiUIt lll.
Cn I l0
5. fpe4a oA 6ykoBuHe (s:0,75) Avrarrp&Ka3aH Ha cnut\v 112. u3pa\y$ai
6. I&pa'ryuaj noBprurlny rr 3aflpeMnqylpecer(oM Ha crll4r I13.
3m sMa rloDpe']Itll fipece(Ter{ufiy rpeae.
lpe4Mera np[ka3agor cBojrM
Cn. 112 Cr. ll3
7. L,3pa'qyaaj sanpeMuBy HeorecaEor ?pynqa lyror 7m, al(o jecpeArhH opeceK fipyra npeqHfiKa 4dm.
8, IbpaqyHaj 3rnpeMIHy 50 jeaEakk,. orecaHkx rpena apyrHx 8m,qlrjlr Je cpe!rbr nppcFr{ KBaApar AyxnHe cTpaHfiue ldn.
9, Kon ko n rapa Botre 3axBata xouKa (c,rxKa ll4), ay6oka 1,6m,aKo je npeqHrk o6pyqa Ha noJoBrHl.r lm?
6 a.ordprj! s VIII pasper
Cn. 1tl
c60
/
82
10. l43paqyFaj 3€npeMuHy 6yJ'era luie cyBeher xpyra "rp6Yxa'je D:1,8m,a BocnEa 6ypera je H:1,5m.
AtMeEsllje: nPerIHtll( Haj-npeqEn( AHa d:1,4 m,
11.
Cr- 114
KomKo ,rxraoa rpoxhaHor coKa caapxti 6aqBa nyra 2m' axo jenpe'tBxK aHa 80im, a npe,[rrn "rp6yxa" l,l0m?
y jeaRoM BxAapcKoM noapyMy HanyrbeHo je 5 jenHaKxx 6a'{Bl'l
BfiHOM. KO,llr(O rrTapa BllHa caapfie OaqBer aKO le aficuHa lea-EaKa 2,{o, npeqr K alla 1,1m tt llpeqsn( HajBeher (pyra
"Tp-6yxa" 1,25m?
l2-
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XIII. 3AAAUL 3A IIOHABJbAIT,E IPAAI'IBA
l4akqa yrnoBr nerocrpaHor porJr,a cy pelo[t 60", 80', 7]' H
45 Kontrkq o)xe 6"r, vrao?
,[a rlr Ko! rrersopocrpaxor porJr,a Mory cBu uBIrqHu yrnost !a 6yaynpaBn? 3alrlro?
3. Vuenrx ie Meplo BtlqHe yrnose porJba u oHrr cy H3lloclrtlpetroM 115', 9i', 84 H 103". llofiaxx !a je florperx[o nptrlrKoMMePersa.
4, JkMeHa (yrxja orBopeHa ca rop6e crpaEe tMa o6nut( npaBoy'rrlor oapanerennnela. ly'3paqyHajTe lbeHe auMeli3lrie axo je Bu-crHa jeAHaka no,roBI,IEIr llll'tp,{H€ Ij rpehr4sfi tryxsBe, a noBp'u Ha ocrarHx ner cTpaHa je 576cmt.
5. Urrra rrMa rrMeE3uje 25cm, 12cm D 6,5cm. Konullo je uurananorpe6fio 3a 3ur \yt 4,2fi, uupofi 3,0m u Bxco( 4,8m?
6. AfijaroHata npaBoyrror napareJlentrneaa je l3cm,,qy)Krlra 4cm a
uprHa 3cm. l43pa,ryHaj noBptrljHy u 3atrpeMtlly napaJrerlclu-IICAA.
7. nonpecHx npece( jerHe rBo3a(f,e ul,nxe je o6nxfia npaBfirHorrueciovrra croaHuue 4cm. XonLko r{ouIa 20m re u{illle atoje cneiu@urni rexuHa rBoxha 7,8g crnd x aKo lkg te ulrnl{eclaje 6 alinapa?
JcaaH o6e,rrrck BucoK 25m qva 06,rlK flpaBtinHe rpocrpaHc DprlJ'J e ocHoBHe fiBuue ln. xonrxa je 3anpeM fia ror ooerHcl{ai
Caflnvft 3a naKoBar6e o6nufia nPaBoyr,lor napareienlnera xoj3a oc;oBy rva KBa4par o6nenrl,eH je oMoloM oa u Hka qfija jeMpexa l,6m:. Konl,lKa je 3anpeM Ha ror caHlryxa axo Je Bral{Ha
aBa nyra ,4yxa ofl !y)l{ 8e/
10. Kapocepnja KaMHoHa lyra ie 2,5m, Illnpolta 2,4m n sucoKa 25cm.Kojruro n" lrarepuja,ra Mo*e ra ctaxe y I6y?
11. 3afipeMrrna npaBurHe rpoclpaBe nlpaMttae 3Hocll l5l,gcmr, a
BuciEa tJ:10?im. Koluri je nonpuruna re nupa rae?
OMoraq rpaBurHe Tpocrpa e nHpaul|ae je 90cm'. Konrxa je 3a-
opeMIHa, aHo je ocdoBHa xBlrua 12 cm?12.
ti4
13.
t4.
16.
17.
18.
l4rpauynarn rexllHy 3iatHoi nprlBccxa y 06,rrrHy npaBfi,tHor re-rpaeapa ocHoBne uBxue l0mm, ako je cneuudx'iHa rexftHa JJla-ra 19,3g/crn3.
I,Ispalynaj nonpuuny n 3anpeMrny npaBrJrHot rerpaeApa ocHoBEexBllqe 6cm.
15. OcnoBna uBErta [paBr.rJrHe hecrocrpase mrpaMule je 8cm, arbeHa 60qHa liB,rua je l0crn. 14:pavynaj noapuuny 3anp.Mr,rHyle nupaMnae.
Do'rHa xBrqa npaBurrHe rxecrocrpane rrpar,ruae je 3cm, Beha orocHoBHe trB ue, I43pa,ryHaj 3anpeMHHy Te n parvtAe aKo je H,cHaBtlcltEa 4cm.
MepMepH[ cnoMeHaK o6,rir'{a n[paMnae HMa 3a ocnoBy poM6 qnjecrpaHnqe oA 4m rpaAe yrao oA 30'. BuciiEa cfioMeEu(a je 5m.Korllku je Dpti?rcaK clloMefluka tla rno axo je cneq!(brqfia te-xriFa MepMepa 2,8kg/dm3?
Mepuepnu cnovenrx HanpaBrbeH je rar{o rc je Ha HouKy rrs'{uelm, nocTaB,beHa jeaHaxoherqfla nrpcuraa 'rrja cc orHoBa nofi-Jlana ce cTpanoM xoure. llspavynaj TexnHy ror crroMenaxa ar(oje cnequ(brqHa rex{nHa MepMepa 2,8kg/dmr.
19. Btrcrlna nrpanrrl4e BxclEe. I43paqyDaj noBpurDHy n
3alpeMrrny npaBurHe:
a) qerBopocrpaHe nupaMuae ocEoBHe nBrrrle 4cm.6) urccrocrpane nupaMrae ocnoBEe fiBrrqe 8cm.
20. Tpa serBprrHe cyna o6,rllka BaJEr{a Koa r{ora je BlrcrHa jelHakanpeqHlr(y ocHoBe Hany6eHo je BoaoM. KoJTrKo je BoAe y cyAyal(o je noBprnffia oiroraqa 25ndmr?
21. qenrqHa rufifika npeqslka ocrioBe ldm, ]Iyra 2m noronu ce yBoay. Konfixo je Nary6r.ra oa cBoje rex,ltre?
lllyn,ra uecrnrana qeB yHyrpanrher npeqErrKa 2cm r Ae6,'b&He3rua 4mm HanyBena je onoBoM crequ(brqHe rer{xHe I l,3g/cm3.Konrl{a je TexrBa qeB{ lyre 6m, al(o je cfieqxaD{qHa rexnHaMecuEra 8,4glcm3?
flpaBoyraos{x Ayr(uHe 2cm lr tllnprrHe l,scil o(pehe ce ol(o ocenaparerrrHe ca aYxr'rHoM Ha yaaJbeHocTn oa 2cm. Korlrka je no-BprrrxHa r.r 3a[peMxna Tako Eaclalor lera.
UeHTpa,lF yrao ovoraqa xyIIe je 120', a fiorynpecrixK ocHoBe15cm. Koflr,rKa je neua noapll:r.rna r.r 3anpeMrrHa?
I{onuxa je usnoanuua ,r BtcnHa Kyne noJrynperlEtKa l5cm, axoje rloBpnrlrHa oMorarra ryne Il,?75dmr
Horu(a je r3BoaHnqa l(yne [onyfipeqH]r(a 2dm aKo je salrpeMuHaI{yne 628cma?
.4-Je ooqHe
22.
23.
24.
25.
28.
85
27. AKo je BrcuHa xyne l1-", .o" i" s MepHx 6poj u3Boaurlqc Kyne," 13fi3pa3r, Kao llyrxqrjy npouerutee s:a) nonynpeqH I( ocEoBe,6) noapuury xyne,q) 3anpeMuHy kyfe.Kao noce6ad c"lyqaj y3Mure s:24cm.
28. l4gsoaa{qa xyne je sa 1cm ayxa o4 nfcure. l4spavynajre no-BpuruHy jl 3anpcMtrrry kyne ako je nonyrJpeqHfiI< ocHoBe Scm.
29. llpaeoyr,rr rpojtao qrja jc jenHa karcra 6cfl a ,pyra 3a 2crDKpaha oa xxnorpHyie o6php ce oxo jclHe, a 3ar v 'oKo lpyrexarerc, Ja r{or Ko ce pa3,1rjl(yjy: a) noBpuJrHe 6J lanpe{uHcTAI(O TACTAJINX TEJ]3.
30. napEu korao o6,rfka BaJbxa 3aBprnaBa ce ca cBoje clpaEe je!-Hov noJyronroM npesllxa 8dm, BajbaK racror flpeqHuKa fiva a\.)r{rHy ,,Ba nyra Behy o! npc'tHfixa ocHoae Barbxa, Ko,ruxa je no_Bpllt Ea I(oTiclKo,rrm€ je 3anpeM{Ha korra?
31. KasaH {Ma 06rrt( Bafi,Ka kojlr ce ca o6e crpane 3aBpruaBa rrony-,rrolraMa fcror npeqtnka, Cfiorbaru]s! npeqnrk Ba;ra je lm-aIberoBa Ay)Krida 2m. Konllka je rextrna ror r(a3aHa al(o ic l1e6-i6[Ha 3[Aa 2crn a cneqn(b{,rHa TexrHa MaTepuja,]ra oA Kor jeHanpaB,'l'eH 7,8 g/cnt?
32. Konlra je 3arpeMuEa l(yrle qrja je noBpuruta oMoraqa 60,,rcms
a norynpeqHllK Je -BllcrlHe I.y!e.
33. Xeaaap qrje ce r&MeH3flje olEoce r{ao_ 1:3:9 nMa jearaxy 3a-npeMllHv ca l<oq(oM r[jaroEare D:3l3cm. 3a l(o.lluno ce pa3-nrl<yiy noBplllnHe Ta aBa rena?
34. 3aflpevllHa npaBllrHe oecrocrpaHe nMpaMnae je 40\3cmt, aBlIcuEa nupaMllle je 5cm. I{Oan(a je EeEa noBplx{Ea?
35. V npaan,rnoj qerBopocrpadoj nIpaMuau ca ocsoBEoM rrBxrIoM l2dmlr BuclrtloM 8dm yrlcaHa je xyna. Ir3paqyHaj:
a) Kaxo ce oArroce noBprrruHe Kyne r nrpaMuAel6) 3a KorxKo ce pa3nnKyjy 3anpefiIrEe rrl,lpaMtAe u (ylre?
36. Oxo npaea,rue qcrBopocrparre nrpaMrAe qkja je nMjarcHanaocfioBe lticn B c Ha 6cm onxcaHa je KJna. Ir3paqyHaj:
a) 3a xornxo ce pa3ntxyjy floBprnufie ra ABa Tena?
6) I{a(o ce oAEoce 3anpeMllse la aBa rena?
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40.
ner jeqHaKfix ,onr{ua nonynpeqHfiKa 2cm rpe6a nperonrrH yy jeaHy ,onrnuy. KoruHlt he 6lrrx no,lyflpeqHfil{ floBe nonrHue?
O6rM Benal(or Kpyra Koa Jlome je l2ncm. I43paqyraj:
a) noBprxxHy nonre,
6) 3anpeMrrEy nofire.
noBplrr.{Ha ocHose xyne je l00Ecm:, a BlrclrHa je 5c'n. I43paqyflajnoaptlJxHy nonre I{oJa ca KynoM uMa JeaHaKy ]aIIpeMDHy.
Aoxalxx na je 3anp€MrHa BaJbKa ylr caHor y Kour{fi jeana no_
?loBllHa 3anpeMIlge aaJblia ool,cafior o(0 Koqfte.I
41, .4oKaxa aa je [IoBptuxEa ,oI]Te yn'lcafle y Koll(y noBpl]llt_
Be rotrTe onlcaEe oKo I(oq(e.
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