  Real foams can be viewed as a geometrically well-organized dispersion of more
or less spherical bubbles in a liquid. When the foam is so drained that the
liquid content significantly decreases, the bubbles become polyhedral-like and
the foam can be viewed now as a network of thin liquid films intersecting each
other at the Plateau borders according to the celebrated Plateau's laws. In
this paper we estimate from below the surface area of a spherically bounded
piece of a foam. Our main tool is a new version of the divergence theorem which
is adapted to the specific geometry of a foam with special attention to its
classical Plateau singularities. As a benchmark application of our results we
obtain lower bounds for the fundamental cell of a Kelvin foam, lower bounds for
the so-called cost function, and for the difference of the pressures appearing
in minimal periodic foams. Moreover, we provide an algorithm whose input is a
set of isolated points in space and whose output is the best lower bound
estimate for the area of a foam that contains the given set as its vertex set.
