posted by Meg on .
PLEASE HELP ME, I HAVE AN EXAM TOMORROW AND THIS THE ONLY QUESTION I HAVE. THE AREA OF A REGULAR HEXAGON IS 35 IN SQUARED. FIND THE LENGTH OF A SIDE. ROUND YOUR ANSWER TO THE NEAREST TENTH. I KNOW THE ANSWER IS 3.7 BUT I DON'T KNOW HOW TO GET IT!!
This site explains how to find the area of a regular hexagon.
IM GOING TO CRY!!!!!!!!!!!!!!!!
But it doesn't say what the apothem or the perimeter is so HOW do I find the length of A side????? The website didn't help at all.
The area is made up of 6 equilateral triangles
look at one of these. call each side x
draw a perpendicular from a vertex to the base, call it h. Makes no difference which one, since all sides are the same
We can find the height h by using Pythagoras
((1/2)x)^2 + h^2 = x^2
(1/4)x^2 + h^2 = x^2
h^2 = x^2 - (1/4)x^2 = (3/4)x^2
h = √3x/2
area of one triangle = (1/2)basexheight
area of whole hexagon = 6(√3/4)x^2 = (3√3/2)x^2
but this equals 35
(3√3/2)x^2 = 35
x^2 = 70/(3√3) = 13.4715
x = 3.67035 , they rounded that off to 3.7