And How They Work

Math 100G Textbook pages 66 - 69

Common Geometric Formulas

Rectangle

Perimeter

P = 2(l) + 2(w)

P = 2(15) + 2(5)

P = 30 + 10

P = 40 cm

5 cm

15 cm Area

A = lw

A = 15(5)

A = 75 cm2

Parallelogram

Perimeter

P = 2a + 2b

P = 2(6) + 2(16)

P = 12 + 32

P = 44 cm

16 cm

6 cm 5 cm

Area

A = bh

A = 16(5)

A = 80 cm2

Trapezoid

Perimeter

P = b + a + B + d

P = 10 + 9 + 17 + 8

P = 44 cm

10 cm

17 cm

9 cm 8 cm 7 cm

Area

A = ½h(B + b)

A = ½(7)(17 + 10)

A = ½(7)(27)

A = (3.5)(27)

A = 94.5 cm2

Triangle

Perimeter

P = s1 + s2 + s3

P = 18 + 14 + 10

P = 42 cm

10 cm

18 cm 14 cm

12 cm

Area

A = ½bh

A = ½(10)(12)

A = (5)(12)

A = 60 cm2

Triangle Angles

Find the measure of angle “a.”

a + b + c = 180°

a + 36 + 73 = 180°

a + 109 = 180°

-109 -109

a = 71° 73°

36°

a°

Rectangular

Solid

Surface Area

SA = 2lw+2wh+2lh

SA = 2(15)(5) + 2(5)(10) + 2(15)(10)

SA = 150 + 100 + 300

SA = 550 cm2

Volume

V = lwh

V = 15(5)(10)

V = 750 cm3

15 cm 5 cm

10 cm

Circle

Circumference

C = 2πr

C = 2(π)(8)

C = 16(π)

C = 50.2654..

C = 50.27 cm

Round answer to the hundredths place.

8 cm

Area

A = πr2

A = (π)(82)

A = (π)(64)

A = 201.0617…

A = 201.06 cm2

Cylinder

Lateral Surface Area

LSA = 2πrh

LSA = 2(π)(4)(20)

LSA = 160(π)

LSA = 502.654…

LSA = 502.65 cm2

20 cm

4 cm

Round answer to the hundredths place.

Surface Area

SA = 2πrh + 2πr2

SA = 2(π)(4)(20) + 2(π)(42)

SA = 160(π) + 32(π)

SA = 192(π)

SA = 603.1852…

SA = 603.19 cm2

Cylinder

(continued)

Volume

V = πr2h

V = (π)(42)(20)

V = 320(π)

V = 1,005.308…

V = 1, 005.31 cm3

20 cm

4 cm

Round answer to the hundredths place.

Cone

Lateral Surface Area

LSA = πrl

LSA = π(9)(15)

LSA = π(135)

LSA = 424.1146…

LSA = 424.11 cm2

15 cm

9 cm

12 cm

Round answer to the hundredths place.

Surface Area

SA = πr2 + πrl

SA = (π)(92) + (π)(9)(15)

SA = 81(π) + 135(π)

SA = 216(π)

SA = 678.5834…

SA = 678.58 cm2

Cone

(continued)

15 cm

9 cm

12 cm

Round answer to the hundredths place.

Volume

V = 1/3πr2 h

V = 1/3(π)(92)(12)

V = 1/3(π)(972)

V = 324(π)

V = 1,017.8751…

V = 1,017.88 cm3

Sphere

Surface Area

SA = 4πr2

SA = 4(π)(32)

SA = 4(π)(9)

SA = 36(π)

SA = 113.0972…

SA = 113.10 cm2

3 cm

Round answer to the hundredths place.

Volume

V = 4/3πr3

V = 4/3(π)(33)

V = 4/3(π)(27)

V = 36(π)

V = 113.0972…

V = 113.10 cm3

Congratulations!

You made it through all of the

Geometric Formulas!!!

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