is there an equation I can use to find the length of a side (L) of a regular hexadecagon (16 sided polygon) based on its radius (by which I mean the length from the center to on vertex) or its diameter (twice that... duh)? That would be really helpful.
2026-03-29 18:51:02.1774810262
how to find the length of a side of hexadecagon in relation to the radius or diameter.
1.2k Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
You can set up a right triangle to solve the problem. Suppose we are given the side length $l$ and that the polygon has $16$ sides. Then we can create a right triangle by joining the center $C$ of the polygon to the midpoint $M$ of one of its sides and then to a vertex $V$ of that same side. Since the polygon has $16$ sides, $$m\angle A=\frac{360^\circ}{32}=11.25^\circ$$ and now we can solve for the hypotenuse of the triangle. Since the short leg of the triangle is half of the side length of the polygon, if we let $h$ be the length of the hypotenuse, we have $$\sin A=\frac{\frac{1}{2}l}{h}$$ $$\sin 11.25^\circ=\frac{l}{2h}$$ $$h=\frac{l}{\sin 11.25^\circ}$$ And this is the formula you're looking for.
If this is difficult to follow, let me know and I'll draw a picture to go with my answer.