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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.