  Let F be a surface and suppose that \phi: F -> F is a pseudo-Anosov
homeomorphism fixing a puncture p of F. The mapping torus M = M_\phi is
hyperbolic and contains a maximal cusp C about the puncture p.
  We show that the area (and height) of the cusp torus bounding C is equal to
the stable translation distance of \phi acting on the arc complex A(F,p), up to
an explicitly bounded multiplicative error. Our proof relies on elementary
facts about the hyperbolic geometry of pleated surfaces. In particular, the
proof of this theorem does not use any deep results in Teichmueller theory,
Kleinian group theory, or the coarse geometry of A(F,p).
  A similar result holds for quasi-Fuchsian manifolds N = (F x R). In that
setting, we find a combinatorial estimate for the area (and height) of the cusp
annulus in the convex core of N, up to an explicitly bounded multiplicative and
additive error. As an application, we show that covers of punctured surfaces
induce quasi-isometric embeddings of arc complexes.
