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

4. Area of a regular polygon Area of a regular polygon The area of a regular polygon is: A = ½ Pa Area Perimeter apothem 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 G F E DC B A H 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. Find its area. a 4 A = ½ Pa = ½ (24)(4) Step 1: Find Perimeter 3 x 8 = 24 Step 2: Use Equation

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 5.2. Find the area of the pentagon. B C A D