Chapter 11.5, Problem 1CYU

To determine

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

Answer to Problem 1CYU

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 scale of both the figures is,

  $\begin{array}{c}k=\frac{4}{8}\\ =\frac{1}{2}\end{array}$

As the polygon are similar then,

  $\begin{array}{l}{k}^2=\frac{A_1}{A_2}\\ {\left(\frac{1}{2}\right)}^2=\frac{A_2}{36{\text{yd}}^2}\\ A_2=\frac{36{\text{yd}}^2}{4}\\ A_2=9{\text{yd}}^2\end{array}$

Then, the area of the figure on the right is $A_2=9{\text{yd}}^2$ .