Chapter 11.5, Problem 19PPS

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 19PPS

The area of the triangle is $15$ and the area of the similar figure is $5.4$ .

Explanation of Solution

Given:

The given Figure is shown in Figure 1

  

Figure 1

Calculation:

Consider the area of the triangle is,

  $\begin{array}{c}A=\frac{bh}{2}\\ =\frac{5\cdot 6}{2}\\ =15\end{array}$

Since, $J^{\prime }{K}^{\prime }{L}^{\prime }$ similar to $\Delta JKL$ then scale factor is,

  $\begin{array}{c}k=\frac{JL}{J^{\prime }{L}^{\prime }}\\ =\frac{5}{3}\end{array}$

Then, according to theorem of similar polygon.

  $\begin{array}{l}{k}^2=\frac{15}{A}\\ {\left(\frac{5}{3}\right)}^2=\frac{15}{A}\\ A=\frac{15\cdot 9}{25}\\ A=5.4\end{array}$

Thus, the area of the triangle is $15$ and the area of the similar figure is $5.4$ .