Approximately 30.47 units
To find the Perimeter of this polygon, we can find by calculating the distance between each point
Considering the points are:
1 (3,2) R (1,2) (7,7) and (-3,-2)
1) Let's calculate the distance between each of them, using the formula of the distance derived from the Pythagorean Theorem.
d1 = (3,2) and (1,2)
d_2 =(1,2) and (7,7)
d_3= (7,7) and (-3,-2)
d_4= (-3,-2) and (3,2)
[tex]\begin{gathered} d_{}=\sqrt{(x_{_2-}x_{1\text{ }})^2+(y_2-y_1)^2^{_{}}} \\ d_{_1=}\sqrt{(1-3)^2+(2-2)^2}=2 \\ d_2=\sqrt{(7-1)^2+(7-2)^2}=\sqrt{61} \\ d_3=\sqrt{(-3-7)^2+(-2-7)^2}=\sqrt{181} \\ d_4\text{ =}\sqrt{(3+3)^2+(2+2)^2}=2\sqrt{13} \end{gathered}[/tex]2) Since we have four points then let's consider them as our vertices, and add those line segments do calculate its Perimeter (2P)
[tex]2P\text{ = 2 +}\sqrt{61}+2\sqrt{13}+\sqrt{181}\text{ }\approx\text{ 30.47}[/tex]Notice that for those radicals are not perfect squares they are irrational so approximating these we have.
