Chapter 11.2, Problem 32PSC

To determine

To find the area of parallelogram.

Answer to Problem 32PSC

The area of parallelogramis $420$ .

Explanation of Solution

Given:

  $Perimeterofparallelogram=154$

Formula Used:

  $\begin{array}{l}Areaofparallelogram=b\ast h\\ b=Base,\\ h=Height\end{array}$

Calculation:

  

  $\begin{array}{l}Perimeter=154,\\ Semiperimeter=77\end{array}$

Let,

  $\begin{array}{l}x=oneside\\ 77-x=otherside\end{array}$

10 and 12 are both altitudes.

Since area is the same using either altitude or side, set them equal.

  $\begin{array}{l}12x=10(77-x)\\ 12x=770-10x\\ 22x=770\\ x=35\end{array}$

Therefore, the one side of the rectangle would be

b = 35 ,

And the other side would be

  $\begin{array}{l}h=75-35\\ h=22\end{array}$

Therefore, the area would be

  $\begin{array}{l}A=b*h\\ A=12*35\\ A=420\end{array}$