In an attempt to characterize the distribution of forms and shapes of nodal domains inwavefunctions,we define a geometric parameter, the ratio p between the area of a domain and its perimeter, measured in units of the wavelength 1/√E. We show that the distribution function P(p) can distinguish between domains in which the classical dynamics is regular or chaotic. For separable surfaces, we compute the limiting distribution and show that it is supported on a compact interval, which is independent of the properties of the surface. In systems which are chaotic, or in random waves, the area-to-perimeter distribution has substantially different features which we study numerically. We compare the features of the distribution for chaotic wavefunctions with the predictions of the percolation model to find agreement, but only for nodal domains which are big with respect to the wavelength scale. This work is also closely related to and provides a newpoint of viewon isoperimetric inequalities.