Kites - 2

A short addition to this post:

Question: It is not hard to see that there can be infinitely many kites with the same area and perimeter. So, is it possible to tile the plane without gaps with mutually non-congruent kites all of the same area and perimeter?

Aspects of non-congruent equiparition have been dealt with in many papers by experts. Some pointers are here and linked pages.

One can ask other variants of this question with say, area-diameter as the quantities shared by the kites.

And what about mutually non-congruent parallelograms/ trapeziums of equal area and perimeter?

Hope to add to this post soon.