The classical spherical cap geometry which is used to define the shape of sessile drops resting on polymer surfaces has a deficiency, since it is a two-parameter model of the three measurable drop dimensions:  contact angle, base radius, and height. In this paper, mathematical expressions for a drop having all three measurable quantities as parameters are derived. The proposed new model is termed as the three-parameter spherical cap geometry. A vapor diffusion model for the drop depending on the two-parameter pseudospherical cap geometry is also developed that is similar to that of Rowan, Newton, and McHale. The evaporation rate of sessile drops of water resting on poly(methylmethacrylate) polymer has been studied by using their recently published precise data. When the present analysis is applied, the drop heights as calculated from the reduced two-parameter pseudospherical cap model fit the experimental data better than those calculated from the classical two-parameter spherical cap model. In addition, the drop volumes as calculated from the three-parameter spherical cap geometry give a linear decrease with time with better regression analysis results than those of the other models.