  We show how to construct half-maximal consistent truncations of 10- and
11-dimensional supergravity to seven dimensions using exceptional field theory.
This procedure gives rise to a seven-dimensional half-maximal gauged
supergravity coupled to $n$ vector multiplets, with $n \neq 3$ in general. We
also show how these techniques can be used to reduce exceptional field theory
to heterotic double field theory.
