  Exactly solvable models of planar polygons, weighted by perimeter and area,
have deepened our understanding of the critical behaviour of polygon models in
recent years. Based on these results, we derive a conjecture for the exact form
of the critical scaling function for planar self-avoiding polygons. The
validity of this conjecture was recently tested numerically using exact
enumeration data for small values of the perimeter on the square and triangular
lattices. We have substantially extended these enumerations and also enumerated
polygons on the hexagonal lattice. We also performed Monte-Carlo simulations of
the model on the square lattice. Our analysis supports the conjecture that the
scaling function is given by the logarithm of an Airy function.
