  Given a finitely presented group $G$ and a surjective homomorphism $G\to
\mathbb{Z}^n$ with finitely presented kernel $K$, we give an upper bound on the
Dehn function of $K$ in terms of an area-radius pair for $G$. As a consequence
we obtain that finitely presented coabelian subgroups of hyperbolic groups have
polynomially bounded Dehn function. This generalises results of Gersten and
Short and our proof can be viewed as a quantified version of results from Renz'
thesis on the second BNSR invariant.
