Hi Dave,

A hexadecagon is a 16 sided polygon. I have also seen it called a hexadecagon or a hexakaidecagon. I assume you mean a regular hexadecagon, one where all the sides are the same length and all the interior angles are equal in size. If you join each vertex of a regular hexadecagon to the centre you partition the figure into 16 congruent triangles. Three of them are in my diagram below and one is labeled as triangle ABC. I also let w be the width of the hexadecagon.

Since the 16 triangles are congruent angle BCA = 360^o/16 = 22.5^o. Since the triangle ABC is isosceles angles ABC and CAB are congruent. Thus angle ABC = (180^o - 22.5^o)/2 = 78.75^o and angle ABD = 2 × 78.75^o = 157.5^o.

The length s you cut each side, for example s = |AB|, depends on how large you want the hexadecagon to be. Look at triangle ABC again.

If P is the midpoint of AB then |PB| = s/2, |CP| = w/2 and angle BCP = 22.5^o/2 = 11.25^o. Hence

tan(11.25^o) = |PB|/|CP| = s/w

and thus

s = 0.1989 w

I hope this helps,
Penny