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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.