Chapter 8, Problem 14CR

To determine

The perimeter and area of the polygon with given vertices.

Answer to Problem 14CR

Perimeter is $20\text{ units}$ .

Area is $21\text{ sq}\text{. units}$ .

Explanation of Solution

Given:

  $W\left(5,-1\right),X\left(5,6\right),Y\left(2,-1\right),Z\left(2,6\right)$

Calculation:

The given points can be plotted on a graph as:

  

Use the ruler postulate to find the length and width of the figure:

Length:

  $\begin{array}{l}l=YW\\ l=\left|2-5\right|\\ l=\left|-3\right|\\ l=3\end{array}$

Now, width will be:

  $\begin{array}{l}w=YZ\\ w=\left|-1-6\right|\\ w=\left|-7\right|\\ w=7\end{array}$

Now, perimeter of the rectangle will be:

  $\begin{array}{l}P=2\left(l+w\right)\\ P=2\left(3+7\right)\\ P=2\left(10\right)\\ P=20\text{ units}\end{array}$

Area of the rectangle will be:

  $\begin{array}{l}A=l\times w\\ A=3\times 7\\ A=21\text{ sq}\text{. units}\end{array}$

Therefore,

Perimeter is $20\text{ units}$ .

Area is $21\text{ sq}\text{. units}$ .