Chapter 11.1, Problem 17PPS

To determine

To calculate: To find the area of parallelogram.

Answer to Problem 17PPS

Therefore, the area of parallelogram is $727.44ft{.}^2$

Explanation of Solution

Given information: The given figure in question.

Calculation:

For the calculation of height of parallelogram,

  $\text{Sum}\text{of}\text{all}\text{the}\text{angles}\text{in}\text{a}{\text{triangle=180}}^{\text{o}}$

Let the angle between hypotenuse and base be $x$

Then,

  $\begin{array}{l}{90}^{\circ }+{30}^{\circ }+x={180}^{\circ }\\ {120}^{\circ }+x={180}^{\circ }\\ x={180}^{\circ }-{120}^{\circ }\\ x={60}^{\circ }\end{array}$

Now, according to the figure,

  

  $\begin{array}{c}\sin \theta =\frac{perpendicular(h)}{hypotenuse}\\ \sin {60}^{\circ }=\frac{h}{30}\\ \frac{\sqrt{3}}{2}=\frac{h}{30}\\ \frac{30\sqrt{3}}{2}=h\\ 15\sqrt{3}=h\\ 25.98ft.=h\end{array}$

For the area of parallelogram,

  $\begin{array}{l}\text{Area = base }\times \text{ height}\\ \text{Area}=28\times 25.98\\ \text{Area}=727.44ft{.}^2\end{array}$