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.
My arrangement does use a central triangle like yours, but I don't connect any segments to the midpoints of either triangle.