It is shown that D. Cohen's inequality bounding the isoperimetric function of a group by the double
exponential of its isodiametric function is valid in the more general context of locally finite simply
connected complexes. It is shown that in this context this bound is ‘best possible’. Also studied are second-dimensional isoperimetric functions for groups and complexes. It is shown that the second-dimensional
isoperimetric function of a group is bounded by a recursive function. By a similar argument it is shown that
the area distortion of a finitely presented subgroup of a finitely presented group is recursive. Cohen's
inequality is extended to second-dimensional isoperimetric and isodiametric functions of 2-connected
simplicial complexes.