1. Areas of Regular Polygons Geometry Unit 4, Lesson 3

2. Regular Polygons Regular Polygon is any Polygon that is both equiangular and equilateral. You can circumscribe a circle about any regular polygon.

3. Regular Polygons (cont.) The center of a regular polygon is the center of the circumscribed circle. Center

4. Regular Polygons (cont.) The radius of a regular polygon is the distance from the center to a vertex Center Radius

5. Regular Polygons (cont.) The apothem of a regular polygon is the perpendicular distance from the center to a side Center Radius Apothem

6. Theorem 5-9: Area of a Regular Polygon The area of a regular polygon is half the product of the apothem and the perimeter. A = ½ap a p

7. Example: Find the area of a regular decagon with a 12.3 in apothem and 8 in sides? –First: What is the number of sides? –Second: Find the perimeter. –Third: Plug into the formula Answer: 492 in 2

8. Example: Find the area of a regular pentagon with the sides of 11.6 cm and apothem of 8 cm Area = ½ (8cm) (11.6 x 5) =232 cm 2