11.5 Areas of Circles and Sectors

CA State Standards8: Solve problems involving

perimeter and area.

19: Use trigonometric functions

21. Prove and solve problems regarding circle parts.

Lesson Goals Find the area of a

sector.

ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

theoremArea of a Circle:

Area of a circle is still measured in square units.

r

2A r

definitionSector of a Circle

The region bounded by two radii and their intercepted arc. (like a piece of pie)

r

Area of a SectorThe ratio of the area A of a sector of a circle to the area of the

circle is equal to the ratio of the measure of the intercepted arc to 360°.

or

Theorem

C B

A

2A r

example

Find the area of the circle

3 m

29 mA

23A

exampleFind the area of the circle

18 ft2A r

281 ftA

29A

exampleFind the area of the sector

X

Z

Y

11 m

2area sector

360

mYZXYZ r

2135360area sector 11XYZ

3638 3

8 121

135o

2142.5 m

exampleFind the area of the sector

24579 cm

R M

L

150o

50 cm

712 2500

N

243753 cm

2area sector

360

mLMLRNM r

2210360 50

example

 

8.5 mr

example

2

Find the diamter of given the area of the

shaded region is 28.3 cm .

C

 

Today’s Assignmentp. 695: 3 – 9, 17, 18, 21, 22, 33