Question

determine the perimeter of the given figure on the coordinate plane. round your answer to the nearest hundredth, if necessary. regular octagon jklmnpqr with coordinates j(-6 - 6\sqrt{2},6), k(-6,6 + 6\sqrt{2}), l(6,6 + 6\sqrt{2}), m( p(6,-6 - 6\sqrt{2}), q(-6,-6 - 6\sqrt{2}), and r(-6 - 6\sqrt{2},-6)

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Calculate side - length using points $J(-6 - 6\sqrt{2},6)$ and $K(-6,6 + 6\sqrt{2})$

$x_1=-6 - 6\sqrt{2},y_1 = 6,x_2=-6,y_2=6 + 6\sqrt{2}$.
$d=\sqrt{(-6-(-6 - 6\sqrt{2}))^2+(6 + 6\sqrt{2}-6)^2}=\sqrt{(6\sqrt{2})^2+(6\sqrt{2})^2}=\sqrt{72 + 72}=\sqrt{144}=12$.

Step3: Calculate perimeter of regular octagon

A regular octagon has 8 equal - length sides. If the side - length $s = 12$, then the perimeter $P=8s$.
$P = 8\times12=96$.

Answer:

96