Exercise 19 Page 620

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

First, we will find any missing lengths from these more recognizable polygons. Then we can calculate the area of the square and the area of the triangle. Finally, we will add the individual areas together to obtain the total area of the figure.

Missing Lengths

In the diagram we can see that the side length of the square is 8cm. Let b be the base of the triangle and let h be the height. Since h is one of the sides in a square, we know it is 8cm. We can use the Segment Addition Postulate to write the equation in terms of b.

Let's solve the equations in the above diagram! 8 cm+b=14cm ⇕ b = 6 cm Now that we have the base and the height of the triangle, let's visualize these shapes separately.

Area of the Square

To find the area of the square, we will substitute s= 8 cm into the formula for the area of a square.

A=s^2

Substitute

s= 8

A=( 8)^2

CalcPow

Calculate power

A=64

The area of the square is 64cm^2.

Area of the Triangle

To find the area of the triangle, we will substitute b= 6 cm and h= 8 cm into the formula for the area of a triangle and simplify.

A=1/2bh

SubstituteII

b= 6, h= 8

A=1/2( 6)( 8)

▼

Evaluate right-hand side

Multiply

Multiply

A=1/2(48)

MoveRightFacToNumOne

1/b* a = a/b

A=48/2

CalcQuot

Calculate quotient

A=24

The area of the triangle is 24cm^2.

Area of the Figure

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

To find the area of the figure, we can add these two values. Area of the Figure 64+24=88cm^2 The area of the figure is equal to 88cm^2, which corresponds to answer B.