# 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.