To discuss how to find the perimeter and area of any polygon, we can consider a general example.

Perimeter

Let's begin by drawing a general polygon in a coordinate plane.

This polygon has four sides and its perimeter is the sum of lengths of these sides. Each side is a segment between two points. If we know the endpoints of a segment, we can calculate its length using the Distance Formula. We can then calculate the perimeter by finding the length of each segment and adding them together.

Area

The area of many polygons, for instance rectangles and triangles, can be calculated directly using a formula. If, for a specific polygon, such a formula is not known, the polygon can be divided into triangles. A polygon with $n$ sides can always be divided into $n - 2$ triangles. We can, for instance, divide the same quadrilateral as above into two triangles.

We can then calculate the area of each triangle using the formula

A = \frac{1}{2} b h .

The total area of the polygon is then calculated by adding the areas of the triangles.

Exercise