Chapter 11.1, Problem 22PPS

To determine

To calculate: The area of the given parallelogram.

Answer to Problem 22PPS

The area of the given parallelogram is $A=471.2c{m}^2$ .

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

  $\begin{array}{c}b=22cm\\ \\ \tan {40}^{\circ }=\frac{18}{h}\\ h=\frac{18}{\left(\tan {40}^{\circ }\right)}\\ =\frac{18}{\left(0.84\right)}=21.42cm\end{array}$

The area of the given parallelogram is

  $\begin{array}{c}A=b\times h\\ =22\times 21.42\\ A=471.24c{m}^2\\ A=471.2c{m}^2\end{array}$

Therefore the area of the given parallelogram is $A=471.2c{m}^2$ .