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)
P=a+b+ a 2 + b 2
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= s 2
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
A= 1 2 bh
b and h are the base and height
Triangle
A= s( s - a )( s - b )( s - c ) where s= a+b+c 2
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
A= b 1 + b 2 2 h
b 1 and b 2 are the lengths of the parallel sides and h the distance (height) between the parallels.
Circle
A=π r 2
r is the radius.

 

Table 3. Volume Formulas
Shape
Formula
Variables
Cube
V= s 3
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

V= 1 3 Ah

A is the area of the base, h is the height.
Sphere
V= 4 3 π r 3
r is the radius.