The diameter of a polygon is defined as the longest distance between any pair of vertices of the polygon.

Partition a unit equilateral triangle into seven regions so that all seven regions have the same polygon diameter.

How small can that diameter be made?

(In reply to Solution? by Steve Herman)

I think you mean similar right trapezoids instead of parallelograms.  Anyways, I come up with a polygon diameter of (-1+sqrt(45))/11 = 0.51893 for your configuration.  But that is still larger than what I have.  

Posted by Brian Smith on 2017-05-28 10:31:08