2. Regular Polygons radius – the distance from the center to a vertex We can center any regular polygon inside of a circle: Regular polygons: -all sides congruent-all angles congruent-convex apothem – perpendicular distance from the center to a side

5. THEOREM 10.6 – Area of a Regular Polygon The area of a regular polygon is half the product of the apothem and the perimeter Areas of Regular Polygons

6. Regular decagon: Find the area of a regular pentagon with 11.6-cm sides and an 8- cm apothem.

7. A regular polygon has a perimeter of 40 cm and an apothem of 5 cm. Find the polygon’s area. A = ½ap = ½(5)(40) = 100 cm 2

8. What is the area of a regular decagon where a=19 s=12.3m What is the area of a regular dodecagon where a=26.1 and s=14cm