Page 676 - Basic College Mathematics with Early Integers

S E C T I O N 9.4 I AREA 653

Then unfold the two halves of the circle and place them together as shown:

p r

p r

r

p r

#
The figure on the right is almost a parallelogram with a base of p r and a
height of r.The area is
A = base # height

T T
#
= 1pr2 r
# 2
= p r
This is the formula for area of a circle.

Area Formula of a Circle
CIRCLE
Area of a circle:
# 2
Area = p 1radius2
A = pr 2
22
radius
(A fraction approximation for is p ) .
7
(A decimal approximation for is 3.14.)p

Example 4 Find the area of a circle with a radius of 3 feet. PRACTICE 4
Find the exact area and an approximation. Use Find the area of the given
3.14 as an approximation for p. 3 ft circle. Find the exact area and

Solution: We let r = 3 ft and use the formula. an approximation. Use 3.14 as
an approximation for p.
A = pr 2
#
= p 13 ft2 2
#
#
= p 9 square ft, or 9 p square ft 7 cm
To approximate this area, we substitute 3.14 for p.
#
#
9 p square feet L 9 3.14 square feet
= 28.26 square feet
The exact area of the circle is 9p square feet, which is approximately
28.26 square feet.
Work Practice 4 Answer
4. 49p sq cm L 153.86 sq cm
Concept Check Use diagrams to decide which figure would have a larger Concept Check Answer
area: a circle of diameter 10 inches or a square 10 inches long on each side. a square 10 in. long on each side