Transverse-energy distributions have been measured for the collisions of the 32S nucleus with Al, Ag, W, Pt, Pb, and U target nuclei, at an incident energy of 200 GeV per nucleon. The shapes of these distribution reflect the geometry of the collisions, including the deformation effects. For central collisions, the transverse-energy production in the region -0.1<ηlab<2.9 increases approximately as A0.5, where A is the atomic mass number of the target. This increase is accompanied by a relative depletion in the forward region ηlab > 2.9. These results are compared with those obtained under similar conditions with incident 16O nuclei. A comparison is also made with the predictions of a Monte Carlo generator based on the dual parton model. Finally, we give estimates of the energy density reached and its dependence on the atomic mass number of the projectile.