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I have a polygon and I only know the length of its sides, how would I go about figuring out what it's points are?

Assume that the first side starts at the origin (0,0) and extends along the x axis to (length of side a,0).

I realise that this is trivial for, say a triangle, but is there a rule that can be used for all polygons?

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No, you can never do this for for any polygon with more than three sides (unless it's degenerate, so that the length of one side is equal to the sum of the lengths of all the other sides -- but then you just get a straight line). For instance, if the polygon has four sides, all the same length, then it can be a square, but it can also be a rhombus with any interior angle.

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Another way to see it: Have you ever had a bookcase collapse? –  Ross Millikan Feb 9 '11 at 13:40
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