# Perimeter and Area

### Contents

#### Perimeter

The perimeter of a shape is the distance around its edges--the distance you would have to travel to walk once around the shape along its edge. In general, the perimeter of a shape is the sum of the lengths of its sides.

#### Perimeter of a Polygon

A polygon is a closed shape made up of several straight line segments. The perimeter of a polygon is the sum of the length of all these sides. For example, the perimeter of the polygon pictured below is equal to 1 + 5 + 4 + 2 + 7 = 19:

Perimeter of a Polygon

#### Perimeter of a Rectangle

A rectangle is a 4-sided polygon in which opposite sides have the same length and all angles have the same measure. Since opposite sides have the same length, we have only to add the lengths of two adjacent sides and multiply by 2 (so each side is "counted" twice). The formula for the perimeter of a rectangle is 2×(h + w), where h and w are the height and width of the rectangle. For example, the perimeter of the rectangle below is 2×(3 + 6) = 2×9 = 18.

Perimeter of a Rectangle

#### Perimeter of a Square

A square is a 4-sided polygon in which all the sides are the same length. Therefore, to find the perimeter of a square, we have only to multiply one side by 4. The formula for the area of a square is s, where s is the length of a side. For example, the perimeter of the square below is 4×8 = 32:

Perimeter of a Square