6th Grade Math Textbook, Progress

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.

A
bh Use the formula for thearea of a parallelogram.

 Cr Substitute b
^12 Cand h
r.

 ( 2 r)r Substitute C
 2 r.


r^2 Simplify.

Find the area of the circular piece of wood.

First estimate: A
r^2

A
 3 (10 ft)^2 
 3 100 ft^2


300 ft^2

Then find the area using 3.14 for .

A
r^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

A
1386 yd^2

1

2

1

2

Area of a Circle:A
r^2

Think

Think: r
18 ft 2 
9 ft

Think

254.34 ft^2 is close to the

estimate of 300 ft^2.

42 yd

Think

r
42 yd 2


21 yd

Find the area of the shaded region.

A
area 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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