Get the side of an hexagon knowing its area?

Question

i need to get the side of an hexagon knowing its area, i think i need to divide it into triangles and do some trigonometric trick, but i cant figure it out, or if there is any other way to do it

Forgot to add, i meant a regular hexagon, thanks for your answers!

Answer 1

I assume you mean a regular hexegon.

From http://mathworld.wolfram.com/Hexagon.html :

A = (3 sqrt3 / 2) s².

Solve for s, you get s = sqrt[2A / (3 sqrt3)].

Answer 2

Start with definitions:

An hexagon is a six-sided figure. A regular hexagon is one where the sides areall equal and each apex falls on a circumscribed circle.

This means that a line joining the centre with an apex is always the same length (the radius of the circle) and the ancgles are all the same.

Because you use the singular "side", I am guessing that you are dealing with a regular hexagon (all sides have the same length, all angles are equal).

Therefore, you can show that the haxgon is made up of 6 identical equilateral triangles joined at their point.

Each triangle will have an area 1/6 that of the total hexagon. Much easier to find the sides of an equilateral triangle knowing its area.

Answer 3

You can do it by dividing the regular hexagon (and I assume you mean a regular hexagon) into six equilateral triangles. Call the length of each side 2x (to avoid fractions) and join the centre to the middle of each side. You can then do pythagoras or trig on this right-angled triangle to get its height in terms of x. This should enable you to work out x from the area. Don't forget to finally double it for side length.

Answer 4

You are right. You need to divide it into triangles and rectangle. For a 30-60 right triangle the sides are 1,sqrt(3),2. If you let the size of the side(hypotenuse) be x then the other sides will be [sqrt(3)/2]X and X/2. Anyway find the area in terms of X then solve for X given the area.