Math CentralQuandaries & Queries


Question from Rick, a parent:

Is there an easy way to figure the even side lengths of a Hexadecagon in layman's
terms, so I know how long to cut the exterior support boards for my pool deck.
The pool is a 16' diameter Hexadecagon and my Wife wants a 4' wide splash deck
all the way around which would make the outside 24' in diameter.


There are a few things we should make clear -- a hexadecagon has 16 sides. Is that really the shape you want? If so, then the angle subtended by a side at the center is 22.5 degrees; we work with half that angle, namely 11.25 degrees.

The word diameter could refer to the distance between opposite vertices, or between opposite edges.

If you mean opposite vertices, then the inner side length will be 16 × sin(11.25) = approx 3.1214'.
The outer side length will be 24 × tan(11.25) = aprox. 4.6822'.

If you mean opposite edges, then the inner side length will be 16 × tan(11.25) = approx 3.1826'.
The outer side length will be 24 × tan(11.25) = aprox. 4.7739'.



Chi's' solution is in agreement with Penny's solution that you mentioned, for the situation where the diameter is measured from side to side. In this note s is the side length that you requested and tan is the tangent of the angle at the centre, in your case an angle of 11.25 degrees. For calculation purposes, the tangent is a button on your calculator.


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