In this presentation, we present a Wachspress-based transfinite formulation on convex polygonal domains for exact enforcement of Dirichlet boundary conditions in physics-informed neural networks. For prescribed Dirichlet boundary function, the transfinite interpolant g lifts functions from the boundary of a two-dimensional polygonal domain to its interior. The trial function is expressed as the difference between the neural network's output and the extension of its boundary restriction into the interior of the domain, with g added to it. Wachspress coordinates for a polygon are used in the transfinite formula, which generalizes bilinear Coons transfinite interpolation on rectangles to convex polygons. Wachspress coordinates serve as a geometric feature map, thereby providing a framework for solving problems on parametrized convex geometries using neural networks. The accuracy of physics-informed neural networks and deep Ritz is assessed on forward, inverse, and parametrized geometric Poisson boundary-value problems.