Chapter 12.2, Problem 2E

a.

To determine

Calculate the area of the parrologram.

Answer to Problem 2E

The area of the parrologram is $22.5$ .

Explanation of Solution

Given:

It is given in the question that the figure is given below:

  

Concept Used:

In this used the concept of area of parrologram .i.e. Area= base $\times$ height

And also using the trigonometric ratio $\sin \theta =\frac{p}{h}$ .

Calculation:

In this here, p is height & h is base.

Now, using the formula of area of parrologram

.i.e. Area= base $\times$ height

  $\begin{array}{l}\sin \theta =\frac{p}{h}\\ \sin {30}^{\circ }=\frac{p}{5}\\ \frac{1}{2}=\frac{p}{5}\\ p=2.5\\ \because \text{area of parrologram =b}\times \text{h}\\ 9\times 2.5\\ 22.5\end{array}$Where p= height

Conclusion:

The area of parrologram is $22.5$ .

b.

To determine

Calculate the area of the parrologram.

Answer to Problem 2E

The area of the parallelogram is $11.646$.

Explanation of Solution

Given:

It is given in the question that the figure is given below:

  

Concept Used:

In this used the concept of area of parrologram .i.e. Area= base $\times$ height

And also using the trigonometric ratio $\sin \theta =\frac{p}{h}$ .

Calculation:

In this here, p is height & h is base. Here the angle is one half so it becomes ${15}^{\circ }$ .

Now, using the formula of area of parrologram

.i.e. Area= base $\times$ height

  $\begin{array}{l}\sin \theta =\frac{p}{h}\\ \sin {15}^{\circ }=\frac{p}{5}\\ 0.2588=\frac{p}{5}\\ p=1.294\\ \because \text{area of parrologram =b}\times \text{h}\\ 9\times 1.294\\ 11.646\end{array}$

Conclusion:

The area of parrologram is $11.646$.

c.

To determine

Calculate the area of the parrologram.

Answer to Problem 2E

The area of the parrologram is $38.925$.

Explanation of Solution

Given:

It is given in the question that the figure is given below:

  

Concept Used:

In this used the concept of area of parrologram .i.e. Area= base $\times$ height

And also using the trigonometric ratio $\sin \theta =\frac{p}{h}$ .

Calculation:

In this here, p is height & h is base.

Now, using the formula of area of parrologram, Here the angle is twice so it becomes ${60}^{\circ }$ .

.i.e. Area= base $\times$ height

  $\begin{array}{l}\sin \theta =\frac{p}{h}\\ \sin {60}^{\circ }=\frac{p}{5}\\ \frac{\sqrt{3}}{2}=\frac{p}{5}\\ p=1.73\times 2.5\\ p=4.325\\ \because \text{area of parrologram =b}\times \text{h}\\ 9\times 4.325\\ 38.925\end{array}$

Conclusion:

The area of parrologram is $38.925$.