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.

http://jwilson.coe.uga.edu/emat6680/parsons/mvp6690/unit/hexagon/hexagon.html

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
= (1/2)x(√3x/2)
= (√3/4)x^2

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

To find the length of a side of a regular hexagon, you need to use the formula for the area of a regular hexagon. The formula is:

Area = (3√3/2) * s^2

where "s" represents the length of a side.

In this case, you are given that the area of the hexagon is 35 in^2. So, let's substitute the value into the formula:

35 = (3√3/2) * s^2

To solve for "s", divide both sides of the equation by (3√3/2):

35 / (3√3/2) = s^2

Now, simplify the fraction on the right side of the equation:

35 * (2/3√3) = s^2

Multiply the numerators:

70 / 3√3 = s^2

To isolate "s", take the square root of both sides of the equation:

√(70 / 3√3) = s

Now, evaluate this expression using a calculator:

s ≈ 3.7 (rounded to the nearest tenth)

Therefore, the length of a side of the regular hexagon is approximately 3.7 when rounded to the nearest tenth.