Page 675 - Basic College Mathematics with Early Integers

652 C HAPTE R 9 I GEOMETRY

Solution: Split the figure into two rectangles. To find the area of the figure, we
find the sum of the areas of the two rectangles.

4 ft

8 ft Rectangle 1 12 4 or 8 ft 5 ft
Rectangle 2

12 ft

Area of Rectangle 1 = lw
#
= 8 feet 4 feet
= 32 square feet
Notice that the length of Rectangle 2 is 12 feet - 4 feet, or 8 feet.

Area of Rectangle 2 = lw
#
= 8 feet 5 feet
= 40 square feet

Area of the Figure = Area of Rectangle 1 + Area of Rectangle 2
= 32 square feet + 40 square feet
= 72 square feet

Work Practice 3

The figure in Example 3 can also be split into two rectangles as shown:
4 ft

Rectangle 1

8 ft
Rectangle 2 5 ft

12 ft

To better understand the formula for area of a circle, try the following. Cut a
circle into many pieces as shown:

p r

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p r

The circumference of a circle is 2pr. This means that the circumference of half a
circle is half of 2pr, or pr.