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Suppose $\Gamma$ is an arithmetic group defined over a global field $K$, thatthe $K$-type of $\Gamma$ is $A_n$ with $n \geq 2$, and that the ambientsemisimple group that contains $\Gamma$ as a lattice has at least twononcocompact factors. We use results from Bestvina-Eskin-Wortman andCornulier-Tessera to show that $\Gamma$ has a polynomially bounded Dehnfunction.

Dehn functions of higher rank arithmetic groups of type $A_n$ in products of simple Lie groups