1. 9.4 Areas of Regular Polygons
February 6, 2008

2. Definitions (associated with regular polygons only)
Center of a polygon – the center of its circumscribed circle.
Radius of a polygon – the radius of its circumscribed circle, or the distance from the center to a vertex.
Apothem of a polygon – distance from the center to any side of the polygon.

3. The center of circle A is: A The center of pentagon BCDEF is:
A radius of circle A is: AF
A radius of pentagon BCDEF is:
An apothem of pentagon BCDEF is: AG B F C A G E D

4. Area of a regular polygon
The area of a regular polygon is:
A = ½ Pa
Area
Perimeter apothem

5. Where does the equation come from?
The apothem is the height of a triangle between the center and two consecutive vertices of the polygon.
you can find the area o any regular n-gon by dividing the polygon into congruent triangles. A H a E G B D C
Hexagon ABCDEF with center G, radius GA, and apothem GH

6. Ex 1: A regular octagon has an apothem. of 4 in. Side length is 3
Ex 1: A regular octagon has an apothem of 4 in. Side length is 3. Find its area.
Step 1: Find Perimeter
3 x 8 = 24
Step 2: Use Equation a 4
A = ½ Pa
= ½ (24)(4)

7. Ex. 2: Finding the area of a regular polygon
A regular pentagon is inscribed in a circle with a side length of 7.5 and an apothem of Find the area of the pentagon. C B D A