The indium-stabilized GaAs(001)-c(8x2) surface was investigated by surface x-ray diffraction and x-ray standing waves. We find that the reconstruction closely resembles the c(8x2) structure described by the recently proposed unified model for clean III-V semiconductor surfaces [Kumpf , Phys. Rev. Lett. 86, 3586 (2001)]. Consistent with this unified model, no In dimers are found for the present surface. Instead, for coverages less than 0.25 monolayers, the In adatoms adsorb at the initially unoccupied hollow sites to form In rows along the  direction. Between the In rows, surface and subsurface Ga dimers are found to coexist in the trench areas. Above 0.25 monolayers, the additional In adatoms fill the trenches and replace the surface Ga atoms. The final structure of the surface layer is essentially identical to the InAs clean surface, except that the In heights are substantially different due to the lateral strain induced by the lattice mismatch. This structural difference explains why the ladder-type pattern observed previously by scanning tunneling microscopy only appears for the In/GaAs(001) and InAs/GaAs(001) surfaces, but not for the InAs clean surface. The structural model we propose for the In-stabilized GaAs(001)-c(8x2) surface, which fully agrees with the scanning tunneling microscopy results, should therefore generally apply to strained InAs(001) surfaces.