Given a regular polygon, you can find its area by dividing the polygon into congruent, non-overlapping, equilateral triangles.

Here a pentagon is separated into 5 congruent, non-overlapping, equilateral triangles.

In order to determine the area of this pentagon, simply determine the area of one triangle, and multiply that number by 5.

5

5

5

5

5

Altitude of a triangle.

3.44

If you have a regular polygon with n sides, you can still divide this polygon into n congruent, non-overlapping, equilateral triangles.

The area of any regular polygon can be given by the following formula.

Here, a represents the apothem of the polygon, and p represents the perimeter of the polygon.

An apothem of a polygon is the altitude of a triangle from the center of the polygon to a side of the polygon.

5

5

5

5

5

Apothem

3.44

2

2

2

2

2

2

√3

Determine the area of this hexagon.

2

2

2

2

2

2

√3

Substitute in values and simplify

Area of the hexagon

4 4

4

4

44

4

Determine the area of this heptagon.

8

Determine the area of this heptagon.

The area of the polygon in practice problem 1 is approximately 48 square units.

The area of the polygon in practice problem 2 is approximately 194 square units.