  In this paper, we compute an upper bound for the Dehn function of a finitely
presented metabelian group. In addition, we prove that the same upper bound
works for the relative Dehn function of a finitely generated metabelian group.
We also show that every wreath product of a free abelian group of finite rank
with a finitely generated abelian group can be embedded into a metabelian group
with exponential Dehn function.
