2. Areas of Regular Polygons 11.2 California State Standards 8 : Solve problems involving perimeter and area. 10: Find area of polygons 16: Perform constructions 19: Use trigonometric functions

3. theorem Area of an Equilateral Triangle s s s

4. informal proof s s 60 o 30 o

5. example 4

6. definition Center of a Polygon The center of its circumscribed circle. Radius of a Polygon The radius of its circumscribed circle.

7. definition Apothem of a Polygon The distance from the center to any side of the polygon. radius apothemapothem

8. definition Central Angle of a Regular Polygon An angle whose vertex is the center and whose sides contain two consecutive vertices.

9. definition The Measure of a Central Angle of a Regular Polygon 72 o

10. theorem Area of a Regular Polygon P is the perimeter a is the apothem s a s s s s

11. informal proof s a s s s s

12. example A regular octagon is inscribed in a circle with a radius 4 units. Find the area of the octagon. 4 22.5 o central angle =45 o b a s 3

13. example A regular octagon is inscribed in a circle with a radius 4 units. Find the area of the octagon. 4 22.5 o 3 a 3.7

14. example The bottom of a glass is a regular dodecagon (12 sides) with a side length of 1.2 cm and a radius of 2.3 cm. What is the area of the bottom of the glass?

15. The bottom of a glass is a regular dodecagon (12 sides) with a side length of 1.2 cm and a radius of 2.3 cm. What is the area of the bottom of the glass? example 1.2 0.6 2.3

16. Today’s assignment p 672: 10 – 32 even Find the area of the triangle. Find the measure of a central angle of a regular polygon with the given number of sides. Find the area of the inscribed regular polygon shown. Find the perimeter and area of the regular polygon. Do the rest at home.