An x-ray scattering study of a laterally structured solid surface wetted by a liquid is reported. GaAs (001) samples with etched trapezoidal surface gratings are used as substrates. Due to the lattice spacing of d = 5900 angstrom and the height h of about 450 angstrom such gratings can be regarded as a row of free edges and wedges. The special wetting behaviour of these wedges with a liquid film of CCl4 was studied using x-ray reflectivity in the region of total external reflection. The reflectivity of the film on top of the laterally structured GaAs substrate is explained by model calculations which contain the electron density depth profile perpendicular to the surface. The thickness of the liquid wetting film on top of the stepped surface was obtained from the fit of the data.