Perimeter of the given polygon is 16.94 units.
To measure the distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by the ex[pression,
Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
By using this expression,
Distance between A(0, 4) and B(2, 0) = [tex]\sqrt{(0-2)^2+(4-0)^2}[/tex]
= [tex]\sqrt{20}[/tex] units
Distance between B(2, 0) and C(2, -2) = [tex]\sqrt{(2-2)^2+(0+2)^2}[/tex]
= 2 units
Distance between C(2, -2) and D(0, -2) = [tex]\sqrt{(0-2)^2+(-2+2)^2}[/tex]
= 2 units
Distance between D(0 -2) and E(-2, 2) = [tex]\sqrt{(0+2)^2+(-2-2)^2}[/tex]
= [tex]\sqrt{20}[/tex] units
Distance between E(-2, 2) and F(-2, 4) = [tex]\sqrt{(-2+2)^2+(2-4)^2}[/tex]
= 2 units
Distance between F(-2, 4) and A(0, 4) = [tex]\sqrt{(-2-0)^2+(4-4)^2}[/tex]
= 2 units
Perimeter of ABCDEF = AB + BC + CD + DE + EF + FA
= [tex]\sqrt{20}+2+2+\sqrt{20}+2+2[/tex]
= [tex]8+2\sqrt{20}[/tex]
= 16.94 units
Therefore, perimeter of the given polygon in the graph attached is 16.94 units.
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