Area of a Circle
13-13
You can use the formulas for circumference of a circle and area of a
parallelogram to help you find the formula for the area of a circle.
The sections of the circle at the right have been
rearranged to approximate a parallelogram.
Abh Use the formula for thearea of a parallelogram.
Cr Substitute b^12 Cand hr.
( 2 r)r Substitute C 2 r.
r^2 Simplify.
Find the area of the circular piece of wood.
First estimate: Ar^2
A 3 (10 ft)^2 3 100 ft^2
300 ft^2
Then find the area using 3.14 for .
Ar^2
3.14(9 ft)^2 3.1481 ft^2
254.34 ft^2
Study these examples.
Find the area.
Estimate: A 3 (20 yd)^2 1200 yd^2
Then solve: A(21 yd)^2
3
A^272 ^211 yd^211 yd
1
A1386 yd^2
1
2
1
2
Area of a Circle:Ar^2
Think
Think: r18 ft 2 9 ft
Think
254.34 ft^2 is close to the
estimate of 300 ft^2.
42 yd
Think
r42 yd 2
21 yd
Find the area of the shaded region.
Aarea of big circlearea of small circle
3.14(13 in.)^2 3.14(9 in.)^2
530.66 in.^2 254.34 in.^2
276.32 in.^2
C
(^12) C
r
b
r h
9 in.
13 in.
d = 18 ft
1.1
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