SOLUTION: The area of a given hexagon is equal to the area of an equilateral triangle whose perimeter is 36 inches. Find the length of a side of the regular hexagon.

Algebra ->  Surface-area -> SOLUTION: The area of a given hexagon is equal to the area of an equilateral triangle whose perimeter is 36 inches. Find the length of a side of the regular hexagon.      Log On


   

Question 1111765: The area of a given hexagon is equal to the area of an equilateral triangle whose perimeter is 36 inches. Find the length of a side of the regular hexagon.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
The area of a given hexagon is equal to the area of an equilateral triangle whose perimeter is 36 inches. Find the length of a side of the regular hexagon.
side of triangle = %28sqrt%283%29%2F4%29%2As%5E2
perimeter = 36 so side = 12in 12^2=144
Area = %28sqrt%283%29%2F4%29%2A144
Area = 36%2Asqrt%283%29
Area of hexagon = 36sqrt%283%29
Area of hexagon = %28sqrt%283%29%2F4%29%2As%5E2+%2A6 s= length of side
36%2Asqrt%283%29= %28sqrt%283%29%2F4%29%2As%5E2+%2A6
s%5E2=24
s=2sqrt%286%29