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Ddavidad · Answer 1 · 2018-08-29T09:06:08+0000

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.

$\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -1}}\quad ,&{{ 2}})\quad % (c,d) &({{ 2}}\quad ,&{{ 4}})\\ &({{ 2}}\quad ,&{{ 4}})\quad % (c,d) &({{ 3}}\quad ,&{{ -2}})\\ &({{ 3}}\quad ,&{{ -2}})\quad % (c,d) &({{ -2}}\quad ,&{{ -3}})\\ &({{ -2}}\quad ,&{{ -3}})\quad % (c,d) &({{ -1}}\quad ,&{{ 2}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}$

$\bf -------------------------------\\\\ d=√([2-(-1)]^2+(4-2)^2)\implies d=√((2+1)^2+(2)^2) \\\\\\ d=√(3^2+2^2)\implies \boxed{d=√(13)}\\\\ -------------------------------\\\\ d=√((3-2)^2+(-2-4)^2)\implies d=√(1^2+(-6)^2)\implies \boxed{d=√(37)}\\\\ -------------------------------\\\\ d=√((-2-3)^2+[-3-(-2)]^2)\implies d=√((-5)^2+(-3+2)^2) \\\\\\ d=√((-5)^2+(-1)^2)\implies \boxed{d=√(26)}$

$\\\\ -------------------------------\\\\ d=√([-1-(-2)]^2+[2-(-3)]^2)\implies d=√((-1+2)^2+(2+3)^2) \\\\\\ d=√((1)^2+(5)^2)\implies \boxed{d=√(26)}$

so, those are their lengths, sum them all up, that's the polygon's perimeter.

What is the peremeter of this polygon? (With picture)-example-1

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