Area = ns² / (4tan[180/n]) for anypolygon with equal sides numbering greater than 3

n = number of sides

s = length of side

This is used with an assumption of degrees being used and not radians for the trigonomic function. I am sure that you can figure out how to convert this to use for radians.

]]>I mean the x-axis cuts a side of the polygon in half.

The 12 in the following equation is the perimeter.

The reason for the :sqrt 3 in the denominator is because all of the

thousands of hexagons inside one another are similar or proportional.

So you can look at the biggest one, and when x is :sqrt 3, then

you want 12dx for that skinny donut area.

The thing that interests me is what happens at all the vertices?

It is surprising it works.