Pythagorean theorem, theory of area

["Rupert"]

A lot of ancient proofs of the Pythagorean theorem depended on the
theory of area, although Stephen Hawking, in "God Created the
Integers", speculates that Pythagoras did it with similar triangles.
>From Hilbert's axioms, is there a natural way to develop the theory of
area without proving the Pythagorean theorem first? The crucial
proposition seems to be that the area of a polygon comes out the same
regardless of which triangulation you use.