Want a hint? Think about a circle bound by an n-sided polygon. What happens to the space between the bounding polygon and the circle as n increases? And when n is infinite?
So of three possible regular tilings, which will be most and least efficient?
(Btw, strictly speaking, I shouldn’t have said tri/hex before, as it’s really just hex tiling.)
You could also use some fancy trig to calculate the efficiency %, but that’s way too much work for me. :)
This is the most efficient (known) packing of 17 unit squares inside a square. If you’re asking why it’s like that, that’s above my math proficiency level.
https://en.wikipedia.org/wiki/Square_packing
See also: https://kingbird.myphotos.cc/packing/squares_in_squares.html