AREA OF CIRCLES, SECTORS AND ARC LENGTHSArea Unit Day 4

Tuesday January 6, 2009

WARM UP

HW ANSWERS P. 443 1-4

1. a = 8; A = 256

2. r = ; A = 100

3. r = ; a = 7/2

4. r = ; A = 24

25

2

27

32

a

½ side

r

45-45-90 radius = hypotenuseapothem = leg½ side = leg = apothem

Square

HW ANSWERS P. 443 5-8

5. a = 3; p = ; A =

6. r = 8; p= ; A =

7. r = ; a = ; A =

8. r=3; a=3/2; A =4

3273

34

30-60-90 radius = hypotenuseapothem = shorter leg½ side = longer leg

318 327

324 348

3

32 34a

½ side

r60°30°

Equilateral

HW ANSWERS P. 443 9-12

9. a = ; p = 24; A =

10. r = 10; p=60; A =

11. r = ; a = ; A =

12. r = ; a = 3; A =

34½ side

30-60-90 radius = hypotenuseapothem = longer leg½ side = shorter leg

32

318

324

3150

372 60°

ar

120°

HexagonEach interior = 120°

324

32

HW ANSWERS P. 443 13, 14

13. a = ;s = 12; p = 3632

kla 24

HexagonEach interior = 120°

33636322

1A

60°a

½ side

r30°

3432

6

30°

k8 k2445°

14. )284)(24(

2

1kkA

2128kA

HW ANSWERS P. 443 15-17

15.

16.

17. a)b) .3090c) 6.18d) .2939e) 2.939

3216

18)10

360(2

1

2

1; AOBAOXBOXAOX

332

AREA OF A CIRCLE

A = r2

r

SECTOR

Sector of a circle is the region bounded by two radii and an arc of the circle.

r

r

AO

B

Sector AOB

AREA OF A SECTOR

AOB is a central angle. r

r

AO

B

Sector AOB is a fraction or part of the whole circle’s areaWhat fraction or part of the circle is sector AOB?

AREA OF A SECTOR

AOB = 90°

r

r

AO

B

Sector AOB is orof circle O

360

90

4

1

AREA OF A SECTOR

AOB = 90°

6

AO

B

Sector AOB is orof circle O

360

90

4

1

Area of sector AOB =¼ the area of circle O

or 9)6(41 2 A

AREA OF A SECTOR FORMULA

r

AO

B

Area of sector AOB =

)(360

2rcentral

A

CIRCUMFERENCE OF A CIRCLE

C = 2r or dr

Circumference measures the length of the outside arc or edge of the circle

ARC LENGTH

Arc Length – a piece of the edge of a circle or a fraction of the circumference.

ARC LENGTH

Arc Length =

)2(360

rcentral

AL

5)10(360

180AL

EXAMPLE 1

Find the area of a sector that has a 40° central angle and a radius of 20 m.

20 m

AO

B

40°

EXAMPLE 2

Find the area of the shaded region in circle O.

10 m

AO

B

120°

HOMEWORK

P. 448 2-12 even, 16 and 26andP. 453 2-16 even

Quiz tomorrow on areas of polygons – you will have the area formulas