Chapter 11.5, Problem 20PPS

To determine

To find: The area of the given Figure and use the segment length to find the area of the similar polygon.

Answer to Problem 20PPS

The area of the triangle is $30$ and the area of the similar figure is $53.3$ .

Explanation of Solution

Given:

The given Figure is shown in Figure 1

  

Figure 1

The value of $W^{\prime }{X}^{\prime }=3$ .

Calculation:

Consider the area of the parallelogram is,

  $\begin{array}{c}A=bh\\ =5\left(6\right)\\ =30\end{array}$

Since, $W^{\prime }{X}^{\prime }{Y}^{\prime }{Z}^{\prime }$ similar to $WXYZ$ then scale factor is,

  $\begin{array}{c}k=\frac{WX}{W^{\prime }{X}^{\prime }}\\ =\frac{6}{8}\\ =\frac{3}{4}\end{array}$

Then, according to theorem of similar polygon.

  $\begin{array}{l}{k}^2=\frac{30}{A}\\ {\left(\frac{3}{4}\right)}^2=\frac{30}{A}\\ A=\frac{30\left(16\right)}{9}\\ A=53.3\end{array}$

Thus, the area of the triangle is $30$ and the area of the similar figure is $53.3$ .