Exercise 6 Page 300

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

In the diagram, we can see that the bases of the trapezoid are 6 inches and 10 inches. The height is 4 inches. We can also see that the length of the rectangle is 10 inches and the width is 10 inches. Let's see the figures separately with all their dimensions labeled!

To find the area of the trapezoid, we will substitute b_1= 6, b_2= 10, and h= 4 into the formula for the area of a trapezoid.

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

SubstituteValues

Substitute values

A=1/2* 4* ( 6+ 10)

AddTerms

Add terms

A=1/2* 4*(16)

Multiply

Multiply

A=1/2* 64

MoveRightFacToNumOne

1/b* a = a/b

A=64/2

CalcQuot

Calculate quotient

A=32

The area of the trapezoid is 32 square inches. To find the area of the rectangle, we will substitute w= 10 and l= 10 into the formula for the area of a rectangle.

A=l * w

SubstituteII

w= 10, l= 10

A= 10 * 10

Multiply

Multiply

A=100

The area of the rectangle is 100 square inches. We now know the areas of both figures!

To find the total area of the figure, we add these two values. Area of the Figure 100+32=132in.^2 The total area of the figure is 132 square inches.