Hi Ed.
The short answer is , where w is the side-to-side width and x is the length of a segment.
We have a nifty little search utility you can use here:
mathcentral.uregina.ca/QQ/QQsearch.html
(A simplified version is on the home page of our site)
If you search on "octagon", you will see my response to Martin, which is titled Making a wooden octagon. On that page, you will see how I've come up with this formula.
Cheers,
Stephen La Rocque.
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