  We use the finite lattice method to calculate the radius of gyration, the
first and second area-weighted moments of self-avoiding polygons on the square
lattice. The series have been calculated for polygons up to perimeter 82.
Analysis of the series yields high accuracy estimates confirming theoretical
predictions for the value of the size exponent, $\nu=3/4$, and certain
universal amplitude combinations. Furthermore, a detailed analysis of the
asymptotic form of the series coefficients provide the firmest evidence to date
for the existence of a correction-to-scaling exponent, $\Delta = 3/2$.
