Question

find the exact perimeter of hexagon abcdef plotted below. a(-6,9) b(5,9) c(8,1) d(2,-6) e(-3,-6) f(-9,1) choose 1 answer: a 16 + 2√73 + 2√85 b 16 + √73 + 2√85 c 16 + √73 + √85 d 46

Explanation:

Step1: Calculate length of AB

Use distance formula for points $A(-6,9)$ and $B(5,9)$. Since $y$-coordinates are same, length $AB=\vert5 - (-6)\vert=11$.

Step2: Calculate length of BC

For $B(5,9)$ and $C(8,1)$, distance $d=\sqrt{(8 - 5)^2+(1 - 9)^2}=\sqrt{3^2+( - 8)^2}=\sqrt{9 + 64}=\sqrt{73}$.

Step3: Calculate length of CD

For $C(8,1)$ and $D(2,-6)$, distance $d=\sqrt{(2 - 8)^2+(-6 - 1)^2}=\sqrt{(-6)^2+( - 7)^2}=\sqrt{36+49}=\sqrt{85}$.

Step4: Calculate length of DE

For $D(2,-6)$ and $E(-3,-6)$, since $y$-coordinates are same, length $DE=\vert2-(-3)\vert = 5$.

Step5: Calculate length of EF

For $E(-3,-6)$ and $F(-9,1)$, distance $d=\sqrt{(-9+3)^2+(1 + 6)^2}=\sqrt{(-6)^2+7^2}=\sqrt{36 + 49}=\sqrt{85}$.

Step6: Calculate length of FA

For $F(-9,1)$ and $A(-6,9)$, distance $d=\sqrt{(-6 + 9)^2+(9 - 1)^2}=\sqrt{3^2+8^2}=\sqrt{9+64}=\sqrt{73}$.

Step7: Calculate perimeter

Perimeter $P=AB + BC+CD+DE+EF+FA=11+\sqrt{73}+\sqrt{85}+5+\sqrt{85}+\sqrt{73}=16 + 2\sqrt{73}+2\sqrt{85}$.

Answer:

A. $16 + 2\sqrt{73}+2\sqrt{85}$