Exercise 42 Page 621

Before we attempt to find the area of the given figure, notice that it can be divided into a parallelogram and a triangle.

First, we will identify all the lengths required to find the area of these two figures. Then we can calculate the area of the parallelogram and the area of the triangle. Finally, we will add the individual areas together to obtain the total area of the figure.

Missing Lengths

First, recall that in a parallelogram opposite sides are the same length. Therefore, the base and the corresponding height of the parallelogram are 15cm and 21cm, respectively. We also see that the base of the triangle is 20 cm and the height is equal to the height of the parallelogram, which is 21 cm.

Now that we have all the lengths, we can consider the areas of the figures separately.

Area of the Parallelogram

To find the area of the parallelogram, we will substitute b= 15 cm and h= 21 cm into the formula for the area of a parallelogram.

A=bh

SubstituteII

b= 15, h= 21

A= 15( 21)

Multiply

Multiply

A=315

The area of the parallelogram is 315cm^2.

Area of the Triangle

To find the area of the triangle, we will substitute b= 20 cm and h=21 cm into the formula for the area of a triangle and simplify.

A=1/2bh

SubstituteII

b= 20, h= 21

A=1/2( 20)(21)

▼

Evaluate right-hand side

Multiply

Multiply

A=1/2(420)

MoveRightFacToNumOne

1/b* a = a/b

A=420/2

CalcQuot

Calculate quotient

A=210

The area of the triangle is 210cm^2.

Area of the Figure

We now know the area of the parallelogram and the area of the triangle.

To find the area of the figure, we can add these two values. Area of the Figure 315+210=525cm^2