Exercise 17 Page 64

To determine the perimeter of the polygon, we must find the sum of its side lengths. This polygon has four vertices, so it is a quadrilateral. Let's draw it in a coordinate plane.

Before we can find the sum of the side lengths, we must find the length of each side. We can use the Distance Formula to do this. Let's start with $\overline{ST}.$ We continue by calculating the length of the other three sides $\overline{TU},$ $\overline{UV},$ and $\overline{VS}.$

Side	Coordinates	$\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$	Length
$\overline{TU}$	$(7,\text{-}2)$ $(7,\text{-}6)$	$\sqrt{(7-7{)}^2+(\text{-}6-(\text{-}2){)}^2}$	$4$
$\overline{UV}$	$(7,\text{-}6)$ $(\text{-}5,\text{-}6)$	$\sqrt{(\text{-}5-7{)}^2+(\text{-}6-(\text{-}6){)}^2}$	$12$
$\overline{VS}$	$(\text{-}5,\text{-}6)$ $(\text{-}5,3)$	$\sqrt{(\text{-}5-\text{-}5{)}^2+(3-(\text{-}6){)}^2}$	$9$

Now, let's calculate the quadrilateral's perimeter. We do so by adding the four sides. The quadrilateral's perimeter is $38$ units.