check the picture below.
so.. simply, use the distance formula, to get their length an add them up, and that's the perimeter of the polygon.
[tex]\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ -1}}\quad ,&{{ 2}})\quad
% (c,d)
&({{ 2}}\quad ,&{{ 4}})\\
&({{ 2}}\quad ,&{{ 4}})\quad
% (c,d)
&({{ 3}}\quad ,&{{ -2}})\\
&({{ 3}}\quad ,&{{ -2}})\quad
% (c,d)
&({{ -2}}\quad ,&{{ -3}})\\
&({{ -2}}\quad ,&{{ -3}})\quad
% (c,d)
&({{ -1}}\quad ,&{{ 2}})
\end{array}\qquad
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}[/tex]
[tex]\bf -------------------------------\\\\
d=\sqrt{[2-(-1)]^2+(4-2)^2}\implies d=\sqrt{(2+1)^2+(2)^2}
\\\\\\
d=\sqrt{3^2+2^2}\implies \boxed{d=\sqrt{13}}\\\\
-------------------------------\\\\
d=\sqrt{(3-2)^2+(-2-4)^2}\implies d=\sqrt{1^2+(-6)^2}\implies \boxed{d=\sqrt{37}}\\\\
-------------------------------\\\\
d=\sqrt{(-2-3)^2+[-3-(-2)]^2}\implies d=\sqrt{(-5)^2+(-3+2)^2}
\\\\\\
d=\sqrt{(-5)^2+(-1)^2}\implies \boxed{d=\sqrt{26}}[/tex]
[tex]\\\\
-------------------------------\\\\
d=\sqrt{[-1-(-2)]^2+[2-(-3)]^2}\implies d=\sqrt{(-1+2)^2+(2+3)^2}
\\\\\\
d=\sqrt{(1)^2+(5)^2}\implies \boxed{d=\sqrt{26}}[/tex]
so, those are their lengths, sum them all up, that's the polygon's perimeter.
