The figure is given in the question.
The coordinates are given as
[tex]A(-3,2),B(1,2),C(3,-1),D(0,-3),E(-4,-3)[/tex]
Now determine the length AB,
[tex]AB=\sqrt[]{(1-(-3))^2+(2-2)^2}=\sqrt[]{4^2}=4[/tex][tex]BC=\sqrt[]{(3-1)^2+(-1-2)^2}=\sqrt[]{4+9}=\sqrt[]{13}[/tex][tex]CD=\sqrt[]{(0-3)^2+(-3-((-1)^2}=\sqrt[]{9+4}=\sqrt[]{13}[/tex][tex]DE=\sqrt[]{(1-(-3)^2+(2-2)^2}=\sqrt[]{16}=4[/tex]
So the perimeter of the figure is the sum of all the sides of the figure.
[tex]AB+BC+CD+DE=4+\sqrt[]{13}+\sqrt[]{13}+4[/tex][tex]8+2\sqrt[]{13}=15.2[/tex]
Hence the perimeter of figure is 15.2.
