Perimeter, Area, and Volume

1. The perimeter of a polygon (or any other closed curve, such as a circle) is the distance around the outside.

2. The area of a simple, closed, planar curve is the amount of space inside.

3. The volume of a solid 3D shape is the amount of space displaced by it.

Some formulas for common 2-dimensional plane figures and 3-dimensional solids are given below. The answers have one, two, or three dimensions; perimeter is measured in linear units, area is measured in square units, and volume is measured in cubic units.

Table 1. Perimeter Formulas
Shape
Formula
Variables
Square
P = 4s
s is the length of the side of the square.
Rectangle
P = 2L + 2W
L and W are the lengths of the rectangle's sides (length and width).
Triangle
a + b + c
a, b, and c are the side lengths.
Right Triangle, with legs a and b (see Pythagorean Theorem)
a and b are the lengths of the two legs of the triangle
Circle
P = C = 2πr = πd
r is the radius and d is the diameter.

 

Table 2. Area Formulas
Shape
Formula
Variables
Square

A = s2
s is the length of the side of the square.
Rectangle
 
A = LW
L and W are the lengths of the rectangle's sides (length and width).
Triangle
b and h are the base and height .
Triangle
a, b, and c are the side lengths and s is the semiperimeter
Parallelogram
 
A = bh
b is the length of the base and h is the height.
Trapezoid
b1 and b2 are the lengths of the parallel sides and h the distance (height) between the parallels.
Circle
A = πr2
r is the radius.

 

Table 3. Volume Formulas
Shape
Formula
Variables
Cube
V = s3
s is the length of the side.
Right Rectangular Prism
V = LWH
L is the length, W is the width and H is the height.
Prism or Cylinder

V = Ah

A is the area of the base, h is the height .
Pyramid or Cone

A is the area of the base, h is the height.
Sphere
r is the radius.