Power dependent transformer core dimensions

Dickfore

There were some "empirical" formulae that we used to calculate the minimum necessary cross-sectional area of a laminated transformer core (If I still remember it from the top of my head it was something as [itex]\frac{A}{1 \, \mathrm{cm}^{2}} = \sqrt{\frac{P}{1 \, \mathrm{W}}}[/itex]).

Does anyone have any info where such relationships come from, and what is the physics behind it?