Chapter 11, Problem 1PT

To determine

To Find: The perimeter and the area of the figure.

Answer to Problem 1PT

The perimeter is $56\text{cm}$ and the area is $164.3{\text{cm}}^2$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

Consider the perimeter of the parallelogram is the sum of length of all the sides as,

  $\begin{array}{c}P=2\left(13+15\right)\\ =2\left(28\right)\\ =56\end{array}$

The height of the parallelogram is,

  $\begin{array}{c}h=\sqrt{{13}^2-7^2}\\ =\sqrt{169-49}\\ =\sqrt{120}\end{array}$

The area of the parallelogram is,

  $\begin{array}{c}A=bh\\ =15\left(\sqrt{120}\right)\\ =164.3{\text{cm}}^2\end{array}$

Thus, the perimeter is $56\text{cm}$ and the area is $164.3{\text{cm}}^2$ .