7.2

What’s The Area?

Pg. 8Areas of Circles and Sectors

7.2 – What’s The Area?Areas of Circles and Sectors

7.8 – AREA OF A CIRCLEa. Cut out the circle given to you by your teacher. Then fold the circle in half. Then in half again. Repeat until you have divided the circle into 16 pieces as shown. Then unfold the circle.

b. Label each radius with the letter "r". Then cut out each of the 16 pieces.

c. Alternate the circle pieces so that it forms a shape similar to a parallelogram. What is the height of the parallelogram?

r

r

r

r

e. Find the area of the parallelogram in terms of the radius, r.

A r r

r

r

r

2A r

Area of a Circle:

2A r

a. Find the area of a circle with radius 6 inches.

2A r

236A in 26A

2A r2121 r

2121 r11un r

22d un

2C r20 2 r

2100A un

10 r

210A

258

2r1212 20

7.11 – SHADED AREAFind the area of the shaded region for each shape below. Leave answers in terms of pi.

Big circle – little circle

24 – 2

2

16 4

12 in2

parallelogram – circle

6 4 – 22

24 4 m2

square – circle

4 4 – 22

16 4 in2

10 m

rectangle – 2 circles 20

20 10 – 22 5

200 50 m2

Sector:

Area of part of a circle

Area of a Sector:

2

A

r degree of arc

360

7.12 – AREA OF SECTORSFind the area of the shaded sector. Leave answers in terms of pi.

22

A

90

360

360A 360

A 2un

26

A

45

360

360A 1620

A 24.5 un

25

A

108

360

360A 2700

A 27.5 un

108

A

2( )2

=

135

360

360A 540

A 1.5un2

26

A

300

360

360A 10800

A 230 ft

300

23

A

315

360

360A 2835

A 27.875 un

315

7.13 – ARC LENGTH VS. AREA OF SECTORWhat are the key differences in the arc length and area of a sector?

Arc Length is length from X to Y along circle

2

x

r

degree

360

Area of sector is part of the area of the circle

2

A

r

degree

360

7.14 – ARC LENGTH VS. AREA OF SECTORFind the arc length and area of the sector. Leave answers in terms of pi.

72

360 28

A

360A 4608

A 212.8 in

72

360 2 8

x

360x 1152

x 3.2 in