  We study straight-line drawings of planar graphs with prescribed face areas.
A plane graph is 'area-universal' if for every area assignment on the inner
faces, there exists a straight-line drawing realizing the prescribed areas.
  For triangulations with a special vertex order, we present a sufficient
criterion for area-universality that only requires the investigation of one
area assignment. Moreover, if the sufficient criterion applies to one plane
triangulation, then all embeddings of the underlying planar graph are also
area-universal. Until now, it is open whether area-universality is a property
of a plane or planar graph.
  We use the developed machinery to present area-universal families of
triangulations. Among them we characterize area-universality of accordion
graphs showing that area-universal and non-area-universal graphs may be
structural very similar.
