Chapter 11.1, Problem 20PPS

To determine

To calculate: The area of the given parallelogram.

Answer to Problem 20PPS

The area of the given parallelogram is $A=58i{n}^2$ .

Explanation of Solution

Given information: The parallelogram is given below.

  

Formula used:

The area of a parallelogram is given by

  $\begin{array}{l}A=b\times h\\ b\text{is}\text{the}\text{base}\text{of}\text{the}\text{parallelogram}\text{.}\\ h\text{is}\text{the}\text{height}\text{.}\end{array}$

Calculation:

From the given information it can be observed that

  $\begin{array}{c}b=12.8in\\ \\ \cos {45}^{\circ }=\frac{h}{6.4}\\ h=6.4\left(\cos {45}^{\circ }\right)\\ =6.4\left(\frac{1}{\sqrt{2}}\right)=4.53in\end{array}$

The area of the given parallelogram is

  $\begin{array}{c}A=b\times h\\ =12.8\times 4.53\\ A=57.98i{n}^2\\ A=58i{n}^2\end{array}$

Therefore the area of the given parallelogram is $A=58i{n}^2$ .