For a locally finite set S in the hyperbolic plane, suppose C is a compact, n-edged two-cell of the centered dual complex of S, a coarsening of the Delaunay tessellation introduced in the author's prior work. We describe an effectively computable lower bound for the area of C, given an n-tuple of positive real numbers bounding its side lengths below, and for n≦ 9 implement an algorithm to compute this bound. For geometrically reasonable side-length bounds, we expect the area bound to be sharp or near-sharp.