Chapter 8.4, Problem 11E

To determine

The perimeter of the polygon with the given vertices.

Answer to Problem 11E

  $22.43$

Explanation of Solution

Given:

The given vertices are:

  $\begin{array}{l}U\left(-2,4\right)\\ V\left(3,4\right)\\ W\left(3,-4\right)\end{array}$

Calculation:

The polygon can be drawn as:

  

The lengths of the sides are:

  $\begin{array}{l}UV:\left|-2-3\right|=5\\ VW:\left|-4-4\right|=8\\ WU:\sqrt{{\left(x_2-x_1\right)}^2-{\left(y_2-y_1\right)}^2}\\ =\sqrt{{\left(-2-3\right)}^2+{\left(4-\left(-4\right)\right)}^2}\\ =\sqrt{89}\\ =9.43\\ TQ:\left|2-\left(-2\right)\right|=4\end{array}$

The perimeter will be:

  $\begin{array}{l}=UV+VW+WU\\ =5+8+9.43\\ =22.43\end{array}$