heronov obrazac

2
1 3RYU·LQD DWURX RXJOD+HURQR RQRY YRE REUD]DF 8WURXJOX$0&MH α = = α VLQ VLQ b h b h c c RGDNOHMH 2 bc 2 ac 2 ab P α = β = γ = VLQ VLQ VLQ +HURQR RQRY YRE REUD]DF ,]WURXJOD$0&MH 2 2 2 x b h - = DL]WURXJOD0%&MH ( 29 2 2 2 x c a h - - = L]RYHGYLMH MHGQDNRVWLVOLMHGL ( 29 cx 2 c a b x cx 2 c a x b x c a x b 2 2 2 2 2 2 2 2 2 2 2 2 + - = - + - = - - - = - ,OL c 2 c a b x 2 2 2 + - = VDGDMHL 2 2 2 2 2 2 c 2 c a b b h + - - = DSRYU·LQDWURXJODMH 2 ch P = WM = + - + + - - = + - - = 2 c 2 c a b b c 2 c a b b c 2 c 2 c a b b c P 2 2 2 2 2 2 2 2 2 2 2 ( 29 ( 29 2 c 2 a b bc 2 c c 2 c bc 2 b a c 2 c 2 c a b bc 2 c 2 c a b bc 2 c 2 2 2 2 2 2 2 2 2 2 2 2 - + + + - - = + - + - + - = ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 = + + - + - + + - = - + - - = 2 c 2 c b a a c b c 2 c b a c b a c 2 c 2 a c b c 2 c b a c 2 2 2 2 ( 29 ( 29 ( 29 ( 29 = + + - + + - + + - + + = 2 c 2 c b a a 2 c b a c 2 c 2 c b a b 2 c b a c 8YHGHPROLVPMHQXGDMH s 2 c b a = + + WM 2 c b a s + + = QD·DIRUPXODVH]QDWQRUHGXNXMH ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 = - - - = - - - = 2 c 2 s 2 a s 2 c 2 c s 2 b s 2 c 2 c 2 s 2 a 2 s 2 c 2 c 2 s 2 b 2 s 2 c P 3RYU·LQDSUDYRXJDRQLND$%()MH ch P = .DNRVXWURXJORYL&)$L'(%SRGXGDUQLWRMH SRYU·LQDSDUDOHORJUDPD$%&'WDNR²HU ch P = 7URXJDR$%&SRGXGDUDQMHVD WURXJORP'&%WHMHWHQMHJRYDSRYU·LQDMHGQDND SRORYLQLSRYU·LQHSDUDOHORJUDPD'DNOHSRYU·LQD WURXJODMH 2 ch P = 2YDIRUPXODYD¹L]DVYDNX VWUDQLFXWURXJODWM 2 ch 2 bh 2 ah P c b a = = = A B D C a b h c α F E x c-x M

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Page 1: Heronov obrazac

.HPDO�+DOLORYLü�SURIHVRU�PDWHPDWLNH�%UþNR 1

33RRYYUU··LLQQD�D�WWUURXRXJJOODD��++HHUURQRRQRY�Y�REREUUDD]]DDFF

8�WURXJOX�$0&�MH� α=⇒=α VLQVLQ bhb

hc

c �RGDNOH�MH�2

bc

2

ac

2

abP

α=β=γ= VLQVLQVLQ

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MHGQDNRVWL�VOLMHGL�� ( ) cx2cabxcx2caxbxcaxb 222222222222 +−=⇒−+−=−⇒−−=−

,OL�c2

cabx

222 +−= �VDGD�MH�L�2222

22

c2

cabbh

+−−= �D�SRYU·LQD�WURXJOD�MH�2

chP = ��WM�

=

+−+

+−−=

+−−=

2

c2

cabb

c2

cabbc

2

c2

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P

22222222222

( ) ( )

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222222222222 −++⋅+−−

=

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AB

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Page 2: Heronov obrazac

.HPDO�+DOLORYLü�SURIHVRU�PDWHPDWLNH�%UþNR 2

( )( )( ) ( )( )( )( )( )( )csbsass

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184

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