Chapter 12.2, Problem 3E

a.

To determine

Calculate the area of the parrologram.

Answer to Problem 3E

The area of the parrologram is $\mathrm{19361.702.}$

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

  $\begin{array}{l}\sin \theta =\frac{p}{h}\\ \sin {75}^{\circ }=\frac{P}{100}\\ \frac{1.73+1}{1.41}=\frac{P}{100}\\ \frac{2.73}{1.41}=\frac{P}{100}\\ P=\frac{27300}{141}\\ P=96.80\\ \because \text{area of parrologram =b}\times \text{h}\\ A=200\times 96.80\\ A=\mathrm{19361.702.}\end{array}$

Conclusion:

The area of parallelogram is $\mathrm{19361.702.}$

b.

To determine

Calculate the area of the parrologram.

Answer to Problem 3E

The area of the parrologram is $12174.$

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 will be halves so it becomes ${37.5}^{\circ }$ .

Now, using the formula of area of parrologram

Here the angle is half so, angle is.

  $\begin{array}{l}\sin \theta =\frac{p}{h}\\ \sin {37.5}^{\circ }=\frac{P}{100}\\ 0.6087=\frac{P}{100}\\ \frac{6087}{10000}=\frac{P}{100}\\ P=60.80\\ \because \text{area of parrologram =b}\times \text{h}\\ A=200\times 60.80\\ A=12174.\end{array}$

Conclusion:

The area of parrologram is $12174.$

c.

To determine

Calculate the area of the parrologram.

Answer to Problem 3E

The area of the parrologram is $10000.$

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 will be twice so it becomes ${150}^{\circ }$ .

Now, using the formula of area of parrologram

Here the angle is twice so, angle is

  $\begin{array}{l}\sin \theta =\frac{p}{h}\\ \sin {150}^{\circ }=\frac{P}{100}\\ \frac{1}{2}=\frac{P}{100}\\ P=50\\ \because \text{area of parrologram =b}\times \text{h}\\ A=200\times 50\\ A=10000.\end{array}$

Conclusion:

The area is parrologram is $10000.$