Exercise 21 Page 335

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 8 centimeters and 12 centimeters, respectively. We can also see that 8 centimeters and 4 centimeters are bases of the trapezoid and 4 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= 8 and w= 12 into the formula for the area of a rectangle.

A=l w

SubstituteII

l= 8, w= 12

A= 8( 12)

Multiply

Multiply

A=96

The area of the rectangle is 96 square centimeters. To find the area of the trapezoid, we will substitute b_1= 8, b_2= 4 and h= 4 into the formula for the area of a trapezoid, and simplify.

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

SubstituteValues

Substitute values

A=1/2( 4)( 8+ 4)

AddTerms

Add terms

A=1/2(4)(12)

Multiply

Multiply

A=1/2(48)

MoveRightFacToNumOne

1/b* a = a/b

A=48/2

UseCalc

Use a calculator

A=24

The area of the trapezoid is 24 square centimeters. We now know the areas of both the rectangle and the trapezoid.

To find the total area of the figure, we add these two values. Area of the Figure 24+96=120cm^2 The total area of the figure is 120 square centimeters.