Formulas

c 2008 Formulas for Polygons and Circles –

2D Shapes • Rectangle b

b

b

height – Area: A = bh – Perimeter: P = 2b + 2h b

b b

b

b

base

• Square b

b

– Area: A = s2 – Perimeter: P = 4s

b

side b

b

b

• Parallelogram b

b

– Area: A = bh – Perimeter: Add up all the sides

b

height b

b

b

b

b

base • Trapezoid

base2 b

b

b

b

b

1 2 h(b1

+ b2) – Area: A = – Perimeter: Add up all the sides

height b b

b

b

b

base1

• Triangle – Area: A = bh 2 – Perimeter: Add up all the sides

b

b

height b

b

b

b

b

base • Circle – Area: A = πr2 – Circumference: C = πD = 2πr

Diameter

1

radius

3D Shapes b

b b

• Cube

b

– Volume: V = s3 – Surface Area: S = 6s2

b b

Side b

• Sphere b

b

4 3 3 πr

– Volume: V = – Surface Area: S = 4πr2 r

• Prism

b b

b

b

Ba s e

b

Height

Base

– Volume: V = πr2 h – Surface Area: S = 2πr2 + 2πrh

• Cone – Volume: V = 31 πr2 h – Surface Area: S = πr2 + πrs where s is the distance from the vertex to the circumference of the base.

s h

r

Height

• Pyramid – Volume: V = 31 Bh where B is the area of the base – Surface Area: S = B+nA where n represents the number of triangular faces connecting the base to the vertex, and A is the area of one triangular face.

Ba

se b

b

• Cylinder

b b

ht

b

b

hei g

– Volume: V = Bh where B is the area of the base – Surface Area: S = 2B + P h where B is the area of the base, P is the perimeter, and h is the height

b

heig ht

2

b

Ba s

e