Answer:
72.14 units
Step-by-step explanation:
Let A(8,13), B(5,-18),C(-6,-6) and D(-2,-5)
Apply the distance formula as;
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Finding the lengths of the segments
For AB
[tex]AB=\sqrt{(5-8)^2+(-18-13)^2} =\sqrt{(-3^2)+(-31^2)} =\sqrt{970} =31.14[/tex]
For BC
[tex]BC=\sqrt{(-6-5)^2+(-6--18)^2} =\sqrt{(-11^2)+12^2} =\sqrt{265} =16.28[/tex]
For CD
[tex]CD=\sqrt{(-2--6)^2+(-5--6)^2} =\sqrt{4^2+1^2} =\sqrt{16+1} =\sqrt{17} =4.12[/tex]
For DA
[tex]DA=\sqrt{(8--2)^2+(13--5)^2} =\sqrt{10^2+18^2} =\sqrt{424} =20.6[/tex]
Finding the perimeter will be;
31.14+16.28+4.12+20.6=72.14 units