Exercise 22 Page p28

The figure is made up of a rectangle and a right triangle. We are given the length of the rectangle, the total length of the base of the figure, and the height of the figure.

To determine the area, we can calculate the area of the triangle and the area of the rectangle separately and add them to get the area of the whole figure.

Rectangle

To find the area of a rectangle, we multiply the length by the width. The width of our rectangle is

3.5 cm

and the length is

5.2 cm .

Let's multiply these values.

A = ℓ \cdot w

SubstituteII

$w = 3.5$ , $ℓ = 5.2$

A = 3.5 \cdot 5.2

Multiply

A = 18.2

The area of the rectangle portion is

18.2 cm^{2} .

Triangle

From the figure, we can see that the height

h

of the triangle is the same as the width of the rectangle,

3.5 cm .

To find the base

b,

we need to subtract the length of the rectangle portion,

5.2 cm,

from the total length of the figure,

8 cm .

h = 8 - 5.2 = 2.8 cm

Now we have enough information to calculate the area of the triangle portion. Recall that the area of a triangle is one half of the product of the base and height.

A = \frac{b \cdot h}{2}

SubstituteII

$b = 3.5$ , $h = 2.8$

A = \frac{3 . 5 \cdot 2 . 8}{2}

Multiply

A = \frac{9 . 8}{2}

CalcQuot

Calculate quotient

A = 4.9

The area of the triangle portion is

4.9 cm^{2} .

Figure

To find the area of the whole figure, we will add the area of the triangle and the area of the rectangle.

4.9 + 18.2 = 23.1 cm^{2}

The area of the figure is

23.1

square centimeters.