Basic Mathematics for College Students

If we divide the circle into more and more pie-shaped pieces, the figure will look

more and more like a parallelogram, and we can find its area by using the formula for

the area of a parallelogram.

Substitute of the circumference for b,the length of the base of the

“parallelogram.” Substitute rfor the height of the “parallelogram.”

Substitute 2Prfor C.

Simplify: and rrr^2.

This result gives the following formula.

1

pr 2  2  1

2



1

2

(2pr)r

1

A^12

2

Cr

Abh

796 Chapter 9 An Introduction to Geometry

o

(a) (b)

h

b

Area of a Circle

The area of a circle with radius is given by the formula

Apr^2

r

EXAMPLE (^3) Find the area of the circle shown on the
right. Give the exact answer and an approximation to the
nearest tenth.
StrategyWe will find the radius of the circle, substitute
that value for in the formula , and evaluate the
right side.
WHYThe variable represents the unknown area of the
circle.
SolutionSince the length of the diameter is 10 centimeters and the length of a
diameter is twice the length of a radius, the length of the radius is 5 centimeters.
This is the formula for the area of a circle.
Substitute 5 for r,the radius of the circle. The notation Pr^2 means Pr^2.
Evaluate the exponential expression.
Write the product so that Pis the last factor.
The exact area of the circle is cm^2. We can use a calculator to approximate the
area.
Use a calculator to do the multiplication: 25 P.
To the nearest tenth, the area is 78.5 cm^2.

A78.53981634

25 p

 25 p

p(25)

Ap( 5 )^2

Apr^2

A

r Apr^2

Self Check 3

Find the area of a circle

with a diameter of 12 feet.

Give the exact answer and an

approximation to the nearest

tenth.

Now TryProblem 33

10 cm