  We study lower semi-continuity properties of the volume, i.e., the surface
area, of a closed Lagrangian manifold with respect to the Hofer- and
$\gamma$-distance on a class of monotone Lagrangian submanifolds Hamiltonian
isotopic to each other. We prove that volume is $\gamma$-lower semi-continuous
in two cases. In the first one the volume form comes from a K\"ahler metric
with a large group of Hamiltonian isometries, but there are no additional
constraints on the Lagrangian submanifold. The second one is when the volume is
taken with respect to any compatible metric, but the Lagrangian submanifold
must be a torus. As a consequence, in both cases, the volume is Hofer lower
semi-continuous.
