Question

Find the perimeter of the polygon with the given vertices. Round your answer to the nearest hundredth.

Answer 1

Perimeter of the given polygon is 16.94 units.

To measure the distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the ex[pression,

Distance = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

By using this expression,

Distance between A(0, 4) and B(2, 0) = $\sqrt{(0-2)^2+(4-0)^2}$

                                                              = $\sqrt{20}$ units

Distance between B(2, 0) and C(2, -2) = $\sqrt{(2-2)^2+(0+2)^2}$

                                                               = 2 units

Distance between C(2, -2) and D(0, -2) = $\sqrt{(0-2)^2+(-2+2)^2}$

                                                                 = 2 units

Distance between D(0 -2) and E(-2, 2) = $\sqrt{(0+2)^2+(-2-2)^2}$

                                                                = $\sqrt{20}$ units

Distance between E(-2, 2) and F(-2, 4) = $\sqrt{(-2+2)^2+(2-4)^2}$

                                                               = 2 units

Distance between F(-2, 4) and A(0, 4) = $\sqrt{(-2-0)^2+(4-4)^2}$

                                                               = 2 units

Perimeter of ABCDEF = AB + BC + CD + DE + EF + FA

                                     = $\sqrt{20}+2+2+\sqrt{20}+2+2$

                                     = $8+2\sqrt{20}$

                                     = 16.94 units

      Therefore, perimeter of the given polygon in the graph attached is 16.94 units.

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