Question

determine the perimeter of the given figure on the coordinate plane. round your answer to the nearest hundredth, if necessary. regular hexagon abcdef with coordinates a(-5\sqrt{3}, 15), b(0, 20), c(5\sqrt{3}, 15), d(5\sqrt{3}, 5), e(0, 0) and f(-5\sqrt{3}, 5) > enter the answer in the space provided. use numbers instead of words.

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Since it's a regular hexagon, all - side lengths are equal. We can find the length of one side and multiply by 6. Let's find the distance between points $A(-5\sqrt{3},15)$ and $B(0,20)$.

Step2: Substitute values into formula

Here, $x_1=-5\sqrt{3}$, $y_1 = 15$, $x_2 = 0$, $y_2 = 20$. Then $d=\sqrt{(0 + 5\sqrt{3})^2+(20 - 15)^2}=\sqrt{(5\sqrt{3})^2+5^2}=\sqrt{75 + 25}=\sqrt{100}=10$.

Step3: Calculate perimeter

The perimeter $P$ of a regular hexagon with side - length $s$ is $P = 6s$. Since $s = 10$, then $P=6\times10 = 60$.

Answer:

60