Which is the nonagon with the least area and which fulfills the following conditions.

  1. The nonagon has to be made from 7 triangles and 3 rectangles, all having side-lengths that are integer numbers.

  2. The nonagon has to be convex with all sides equal and their length has to be an integer number. A geometric presentation is required, showing all the lengths.


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All sides are of length 1.
As the three rectangles (obviously) and 7 triangles have minimal areas, so has their sum.
To show trianges have minimal area use Heron's formula 16A^2 = (a+b-c)(a-b+c)(-a+b+c)(a+b+c). With a=b=c=1 this gives 3 and from this representation it is obvious that that is the minimum for non-degenerate integer-sided triangles.


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