How to calculate the radius of a circle inscribed in a regular hexagon? If I know how long one side of a regular hexagon is, what's the formula to calculate the radius of a circle inscribed inside it?
Illustration:


Using the Pythagorean theorem you can turn the hexagon into 12 30-60-90 triangles or 6 equilateral triangles
Hypotenuse squared - half the hypotenuse squared = the length of the radius of the circle (squared) 
Diagram. The red lines are the hypotenuses and the yellow lines are radii of the circle.
