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telltree January 21st, 2010 12:51 PM

Det. length of sides of polygon from Area and ratio of sides
 
Hi everyone. Here is an interesting problem that I posed to myself - but I haven't answered it yet.

Let's say we have a given area A of a convex polygon with n sides and we are also given the extended ratio of all of its sides l1 : l2 : l3 : ... : ln

What are the length of the sides?

Obviously the side ratios would need to be scaled by some factor k to obtain the actual lengths kl1, kl2, . . . , kln

The only two general formulas I know for relating polygon side lengths and areas are based on coordinate geometry or exterior angles. Any ideas?

: )

-Eric


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