1. Areas of Circles and Sectors 11.5 California State Standards 8: Solve problems involving perimeter and area. 19: Use trigonometric functions 21: Prove and solve problems regarding circle parts.

2. theorem Area of a Circle A =   r 2 Area of a circle is still measured in square units r

3. definition Sector of a Circle The region bounded by two radii and their intercepted arc. (like a piece of pie) r

4. C theorem Area of a Sector The ratio of the area of a sector to the area of the circle equals the ratio of the measure of the intercepted arc to 360 o. B A

5. example Find the area of the circle 3 m3 m

6. example Find the area of the circle 18 ft

7. example Find the area of the sector X Z Y 11 m 135 o

8. example Find the area of the sector R M L 150 o 50 cm N

9. example Find the area of the shaded region 4 cm 4 2

10. example You are cutting the front face of a grandfather clock out of wood. What is the area of the front of the case?

11. example You are cutting the front face of a grandfather clock out of wood. What is the area of the front of the case? semicircle rectangle 70 in 21 in 10 in 11 in 42 in

12. example You are cutting the front face of a grandfather clock out of wood. What is the area of the front of the case? 11 21 in

13. example You are cutting the front face of a grandfather clock out of wood. What is the area of the front of the case? 70 in 42 in 10 in

14. example You are cutting the front face of a grandfather clock out of wood. What is the area of the front of the case?