Chapter 11.1, Problem 14PPS

To determine

To calculate: Find the perimeter and area of parallelogram.

Answer to Problem 14PPS

The area and perimeter of parallelogram is $1440i{n}^2$ and $170in$ respectively.

Explanation of Solution

Given information: The given figure in question.

Calculation:

For the area of parallelogram, $\begin{array}{l}\text{Area = base }\times \text{ height}\\ \text{Area}=40\times 36\\ \text{Area}=1440i{n}^2\end{array}$

Use the Pythagoras theorem to calculate the length of parallelogram,

  $\begin{array}{l}{a}^2+b^2=c^2\\ {27}^2+{36}^2=c^2\\ 729+1296=c^2\\ 2025=c^2\\ \sqrt{2025}=c\\ 45in=c\end{array}$

Now, for the perimeter of parallelogram,

  $\begin{array}{l}\text{Perimeter }=2\times \text{( length+ breath)}\\ \text{Perimeter }=2\times (40+45)\\ \text{Perimeter }=2\times (85)\\ \text{Perimeter }=170in\end{array}$