Question

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 1

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.
equilateral triangle perimeter 36 inches
each side eq. triangle then 12 inches
height eq. triangle = sqrt(12^2 - (1/2*12)^2) = sqrt(144 - 6^2)
height eq. triangle = sqrt(144 - 36) = sqrt(108)
height = sqrt(36*3) = 6sqrt(3)
area eq. triangle = 1/2 * base * height = 1/2 * 12 * 6sqrt(3)
area eq. triangle = 36sqrt(3)
( area of an equilateral triangle = side^2 * sqrt(3)/4

36sqrt(3) * 4/sqrt(3) = side^2
144 = side^2
12 = side as stated above )
hexagon area = 36sqrt(3)
hexagon is made of 6 equilateral triangles each with 6sqrt(3) as their area
(6 * 6sqrt(3) = 36sqrt(3)
hexagon eq. triangle area = 6sqrt(3)
6sqrt(3) = side^2 * sqrt(3)/4
6sqrt(3) * 4/sqrt(3) = 24 = side^2
2sqrt(6) = side = length of the side of the regular hexagon


This one is lengthy so be mindful this is an example.
Hope it helps Brittney (:

Answer 2

Thank you everyone for answering my questions, even on my others!