Hi,

I would like to know the FORMULA that I would use to calculate the DIAMATER ('D') of a circle that would fit perfectly within a HEXAGON.

If you are given that the sides of the Hexagon have LENGTH 'L'.

What is the Diameter of a Circle that would fit perfectly within the Hexagon so that the circle just touched the CENTER of each side of the Hexagon?

Thank you!
Kevin

A hexagon has 6 sides. So, if we draw a right triangle from the center of the circle to the

midpoint of a side of the hexagon, we see that tringle has angle 30 degrees.

R=radius of circle.

So, we have R=\frac{L}{2tan(30)}=\frac{\sqrt{3}L}{2}

The diameter of said circle would be twice that.

So, the diameter of the circle in terms of the side length of the hexagon would be

D=\sqrt{3}L

[Glactucus, thank you for your help. I have sent some 'support' your way. Best, Kevin