Chapter 11.5, Problem 1BCYP

To determine

To find: The area of the figure on the right.

Answer to Problem 1BCYP

The area of the figure on the right is $13.5{\text{ft}}^2$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

Two polygons are similar only when the corresponding angles are equal and congruent and corresponding side length are in proportion.

Consider the area of the given figure is of the form,

  $A=\frac{bh}{2}$

Then, the area of the figure on the left is,

  $\begin{array}{l}13.5{\text{ft}}^2=\frac{6\text{ft}\left(h\right)}{2}\\ h=4.5\text{ft}\end{array}$

Since, the given figures are in proportional then,

  $\begin{array}{l}\frac{6}{8}=\frac{4.5}{x}\\ x=\frac{8}{6}\left(4.5\right)\\ x=6\text{ft}\end{array}$

Then, the area of the figure on the right is,

  $\begin{array}{c}A=\frac{1}{2}\left(6\text{ft}\right)\left(4.5\text{ft}\right)\\ =13.5{\text{ft}}^2\end{array}$