Hey!
This is an interesting panelling exercise, although getting them for the same sizes would quiet difficult to achieve, as they might result in deforming the original shape.
How I would do is that get this shape into a proper triangulated mesh and find the dual of it. That should give you the hexagons for sure but not of equal dimensions for sure.
Run a Kangaroo Simulation that would relax and bring the hexagon constraints to the edge lengths of the hexagons.