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.