Chapter 12.9, Problem 9WE

To determine

Find the area of a parallelogram that has $45°$ included angle and side lengths $10\text{ and 18}$ .

Answer to Problem 9WE

The area of parallelogram is $127\text{ sq}\text{. units}$ .

Explanation of Solution

Given information: The given parallelogram has $45°$ included angle and side lengths $10\text{ and 18}$ .

Calculation: Since the given parallelogram has $45°$ included angle and side lengths $10\text{ and 18}$ respectively. Therefore, the area $\left(A\right)$ of triangle formed by these sides and included angle is evaluated from the formula,

  $\begin{array}{c}A=\frac{1}{2}ab\sin \left(C\right)\\ =\frac{1}{2}\left(10\right)\left(18\right)\sin \left(45\right)\\ =63.639\text{ sq}\text{. units}\end{array}$

Now the parallelogram so formed by these sides and included angle will have twice the area of triangle obtained. Therefore area of parallelogram is,

  $\begin{array}{c}\text{Area of parallelogram}=2\left(A\right)\\ =\left(2\right)\left(63.639\right)\\ \approx 127\text{ sq}\text{. units}\end{array}$