Exercise 22 Page 335

Divide the given figure into recognizable polygons.

90in.^2

Practice makes perfect

Before we try to find the area of the given figure, notice that the figure can be divided into a rectangle and a trapezoid.

In the diagram, we can see that the length and width of the rectangle are 10 inches and 5 inches, respectively. We can also see that 10 inches and 6 inches are bases of the trapezoid and 5 centimeters is the height of the trapezoid. Let's see the figures separately with all their dimensions labeled!

To find the area of the rectangle, we will substitute l= 10 and w= 5 into the formula for the area of a rectangle.

A=l w

SubstituteII

l= 10, w= 5

A= 10( 5)

Multiply

A=50

The area of the rectangle is 50 square inches. To find the area of the trapezoid, we will substitute b_1= 10, b_2= 6 and h= 5 into the formula for the area of a trapezoid, and simplify.

A=1/2h*(b_1+b_2)

SubstituteValues

Substitute values

A=1/2( 5)( 10+ 6)

AddTerms

Add terms

A=1/2(5)(16)

Multiply

A=1/2(80)

MoveRightFacToNumOne

1/b* a = a/b

A=80/2