Chapter 12.9, Problem 10WE

To determine

Find the area of a rhombus that has the perimeter 48 and an angle of $55°$ .

Answer to Problem 10WE

The area of rhombus is $118\text{ sq}\text{. units}$ .

Explanation of Solution

Given information: The given rhombus has perimeter 48 and an angle of $55°$ .

Calculation: Since the four sides of a rhombus are equal. Therefore according to question if $\left(x\right)$ is the side of rhombus then its perimeter $\left(P\right)$ is given as,

  $\begin{array}{c}P=4x\\ 48=4x\\ \text{or, }x=12\end{array}$

Now each side of rhombus is 12 units and an angle is $55°$ . Therefore using the formula for area of rhombus having each side $\left(x\right)$ and an angle $\left(\theta \right)$ ,

  $\begin{array}{c}\text{Area of rhombus}=x^2\left(\sin \left(\theta \right)\right)\\ ={\left(12\right)}^2\left(\sin \left(55\right)\right)\\ \approx 118\text{ sq}\text{. units}\end{array}$