Chapter 11.1, Problem 3CYU

To determine

To calculate: The perimeter and area of the given parallelogram.

Answer to Problem 3CYU

The perimeter is $P=64cm$ and the area of the given parallelogram is $A=207.8c{m}^2$ .

Explanation of Solution

Given information: From the given figure it can be observed that in the parallelogram $l=20cm,b=12cm,\theta ={60}^{\circ }$ .

Formula used:

The Perimeter and area of a parallelogram is given by

  $\begin{array}{l}P=2\left(l+b\right)\\ A=b\times h\\ b\text{is}\text{the}\text{base}\text{of}\text{the}\text{parallelogram}\text{.}\\ l\text{is}\text{the}\text{side}\text{adjacent}\text{to}\text{the}\text{base}\left(b\right)\text{of}\text{the}\text{parallelogram}\text{.}\\ h\text{is}\text{the}\text{height}\text{of}\text{the}\text{parallelogram}\text{.}\end{array}$

Calculation:

The given information is

  $l=20cm,b=12cm,\theta ={60}^{\circ }$

Also to find the height of the parallelogram, $\text{Consider}\text{the}\text{Δ}\text{inscribed}\text{in}\text{Parallelogram}\text{.}$

  $\begin{array}{l}\sin \theta =\frac{h}{l}\\ \sin {60}^{\circ }=\frac{h}{20}\\ h=20\times \frac{\sqrt{3}}{2}=17.32cm\end{array}$

Then the perimeter of the parallelogram is

  $\begin{array}{c}P=2\times (l+b)\\ P=2\times (20+12)\\ =2\times (32)\\ P=64cm\end{array}$

And the area of the parallelogram is

  $\begin{array}{c}A=b\times h\\ \text{=12}\times 17.32\\ A=207.84c{m}^2\\ A=207.8c{m}^2\end{array}$

Therefore the perimeter is $P=64cm$ and the area of the given parallelogram is $A=207.8c{m}^2$ .