Let's say 3 sides of a triangle enclose an area of A.
If you add 3 more sides to get a hexagon, you double the perimeter (and therefore construction costs), but the area enclosed is 6A (6 of the original triangles fit in the new hexagon).
If you add 3 more sides to get a hexagon, you double the perimeter (and therefore construction costs), but the area enclosed is 6A (6 of the original triangles fit in the new hexagon).
The chamber size is fit to purpose; smaller cells for incubating worker bee larvae, larger cells for drones and queens.
Even for honey and nectar storage, the cells are sized to a single serving (fortunately roughly the same size as a hatchery cell), so the bees can consume what they need while the rest stays safely sealed with wax caps.