Chapter 11.1, Problem 23PPS

To determine

To Find: To find the area of the given parallelogram.

Answer to Problem 23PPS

The answer is 3,9942 square miles.

Explanation of Solution

Given information: Given sides of parallelogram is 394miles and 158miles.

Formula used: Area of parallelogram $=\text{base}\times \text{height}$

Calculation:

Let the given parallelogram is ABCD where $\angle D=116°$

Join BD, now

First to calculate the height of the parallelogram

Since the diagonals bisect the angles

Therefore,

In triangle ABD

  $\begin{array}{l}\mathrm{Tan}58°=\frac{\text{Height}}{\text{Base}}\\ 1.6=\frac{\text{Height}}{158}\\ 1.6\times 158=\text{Height}\\ \therefore \text{height}=\text{252}\text{.8}\end{array}$

Thus, height is 252.8miles

  $\begin{array}{c}\text{Area}=158\times 252.8\\ =39942.4\end{array}$

Hence, the required area is 39942 square miles.