algebra formulas from geometry

8/9/2019 Algebra Formulas From Geometry

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AL G E B R A

A S elf-T utorial



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This document is intended to present typical formulas from geometry.

Students in algebra or calculus (or other higher math classes) will

encounter them when doing word problems. This is NOT meant as a

formal, detailed lesson in geometry, just an informal review. No examples

of the use of the formulas are given, although a few more details will be

provided on the video version of this Lesson.

A NGLES

F Two angles are Com p l im en t a r y Ang l es if the sum of the measures of

their angles is 90°.

α + β = 90°

F Two angles are Supp l em en ta r y Ang l es if the sum of the measures of

their angles is 180°.

α + β = 180°

…In the following formulas, height is also called altitude.

T RIANGLES

s1 s2

Perimeter: P = s1 + s2 + s3

s3 <Add the lengths of all 3 sides>

α β

α β



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h = height b = base

Area:

F An I soscel es Tr i a n g l e has two sides that are of the same length.

F An Equ i l a t er a l T r i a ng l e has all three sides of the same length.

Y The sum of the measures of the interior angles of any triangle is 180°.

α + β + γ = 180°

F A R i g h t T r i a n g l e has one interior angle equal to 90°.

F The Pyth a gor ea n T h eor em states: For any right triangle, the sum of

the squares of the lengths of the legs is equal to the square of the length of

the hypotenuse.

hypotenuse

leg

leg

OR…

h

b

γ α

β

90°



4

a

b

Y Pythagorean Triples. Here are some examples of combinations of integers that make the Pythagorean equation true:

a b c

3 4 5

5 12 13

7 24 25

8 15 17

9 40 41

Y The sides of similar triangles are proportional.

a b d

f

c

Q UADRILATERALS (Four-sided figures)

Y Square:

s s = side d = diagonal

s s d =

Perimeter: P = 4 s

s

c

e

d



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s Area:

s

Y Rectangle:l = length w = width d = diagonal

Perimeter: P = 2l + 2w

w Area:

Y Parallelogram:

b b= base s = slant height

s s Perimeter: P = 2b + 2 s

b

h = height

Area:

b

Y Trapezoid: s2

s1 s3 Perimeter: P = s1 + s2 + s3 + s4

<Add the lengths of all 4 sides>

s4

l

l

d

l

h

ww



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b2 b1 = first base b2 = second base

h = height

Area:

b1

In calculus, you may encounter trapezoids “on their sides:”

h1 = first height h2 = second height

b = base

h1 h2 Area:

b

Y The sum of the measures of the interior angles of any quadrilateral is

360°.

α + β + γ + δ = 360°

C IRCLES

r = radius d = diameter C = circumference

Diameter: d = 2r Circumference: C = 2πr

or C = πd

r

h

γ

α

β

δ

d



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Area:

π 3.14159265358979323846264338327950288419716939937510…

π <Pronounced: “pie”> is the number of diameters that can fit on the

circumference of a circle.

and 3.14 are typical approximations of π.

S OLID F IGURES Y Cube:

s = side of cube d = diagonal of face

D = diagonal of cube

s Surface Area:

Volume:

s

Y Rectangular Box (or Rectangular Parallelepiped):

= length w = width h = height

d = diagonal of box

Surface Area: SA = 2( w + wh + h)

r

D

d

dh

w



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Volume:

Y Prisms (any kind):

h = height A = Area of the base

Volume:

The video illustrates other examples of prisms.

Y Pyramids (any kind):

h = height A = Area of the base

Volume:

The video illustrates other examples of pyramids.

Y Cone (Right Circular Cone):

s = slant height h = height

r = radius

Lateral Surface Area (Area of cone

not counting the area of base):

h

w

h

h

s

A

r

h

A



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Total Surface Area:

or

Volume:

Y Cylinder (Right Circular Cylinder):

r = radius h = height

Lateral Surface Area:

Total Surface Area:

Volume:

h

r

h

r

r



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Y Sphere:

r = radius

Surface Area:

Volume:

E ND O F L ESSON

r

r

algebra formulas from geometry

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