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Hello,

I have an irregular hexagon whose interior angles are all $2\pi/3$. That is, every pair of opposite edges are parallel. I have the distance between every pair of opposite edges, and I wish to find the perimeter of the hexagon. Intuitively, this seems possible, but I'm not sure how to do it. Also, is there a name for such a hexagon?

If that helps, I can also assume that every pair of opposite edges have the same length.

Many thanks, Adam

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 The opposite edges should not have the same lengths. For instance, the edge lengths may be $a$, $b$, $a$, $b$, $a$, $b$ in a cyclic order. You may also add up this sequence and $c$, $d$, $e$, $c$, $d$, $e$... – Ilya Bogdanov Nov 22 at 15:44
Indeed. Thanks for the correction. An answer to either case would be helpful (either assuming that opposite edges have the same length or not). – Adam Sheffer Nov 22 at 16:51
This question might get a better reception at math.stackexchange.com – Gerry Myerson Nov 22 at 21:57

closed as too localized by Anton Petrunin, Emil Jeřábek, Ryan Budney, Douglas Zare, jc Nov 22 at 16:54

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