Answer:
16.5 units (nearest tenth)
Step-by-step explanation:
Given vertices:
The perimeter of a two-dimensional shape is the distance all the way around the outside.
To find the perimeter of the quadrilateral PQRS, find the lengths of each side by using the distance formula and add them together.
Distance between two points
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points.}[/tex]
[tex]\begin{aligned}\implies \sf PQ & = \sqrt{(x_Q-x_P)^2+(y_Q-y_P)^2}\\& = \sqrt{(2-2)^2+(3-2)^2}\\& = \sqrt{0^2+1^2}\\& = \sqrt{1}\\& = 1\end{aligned}[/tex]
[tex]\begin{aligned}\implies \sf QR & = \sqrt{(x_R-x_Q)^2+(y_R-y_Q)^2}\\& = \sqrt{(-2-2)^2+(-2-3)^2}\\& = \sqrt{(-4)^2+(-5)^2}\\& = \sqrt{16+25}\\& = \sqrt{41}\end{aligned}[/tex]
[tex]\begin{aligned}\implies \sf RS & = \sqrt{(x_S-x_R)^2+(y_S-y_R)^2}\\& = \sqrt{(-2-(-2))^2+(3-(-2))^2}\\& = \sqrt{0^2+5^2}\\& = \sqrt{25}\\& = 5\end{aligned}[/tex]
[tex]\begin{aligned}\implies \sf SP & = \sqrt{(x_P-x_S)^2+(y_P-y_S)^2}\\& = \sqrt{(2-(-2))^2+(4-3)^2}\\& = \sqrt{4^2+1^2}\\& = \sqrt{16+1}\\& = \sqrt{17}\end{aligned}[/tex]
Therefore:
[tex]\begin{aligned}\implies \sf Perimeter & = \sf PQ + QR + RS + SP\\& = 1 + \sqrt{41} + 5 + \sqrt{17}\\& = 6 + \sqrt{41} + \sqrt{17}\\& = 16.5262...\\& = 16.5 \:\: \sf units \:(nearest \:tenth)\end{aligned}[/tex]
Learn more about the distance formula here:
https://brainly.com/question/28144723
