Chapter 8.4, Problem 13E

To determine

The perimeter of the polygon with the given vertices.

Answer to Problem 13E

  $16.92$

Explanation of Solution

Given:

The given vertices are:

  

Calculation:

The lengths of the sides are:

  $\begin{array}{l}PL=\sqrt{{\left(1-\left(-1\right)\right)}^2+{\left(4-\left(-2\right)\right)}^2}=\sqrt{40}=6.32\\ LM:\sqrt{{\left(4-1\right)}^2+{\left(0-4\right)}^2}=\sqrt{25}=5\\ MN:\left|4-2\right|=2\\ NP:\sqrt{{\left(-1-2\right)}^2+{\left(-2-0\right)}^2}=\sqrt{13}=3.60\end{array}$

The perimeter will be:

  $\begin{array}{l}=PL+LM+MN+NP\\ =6.32+5+2+3.60\\ =16.92\end{array}$