Reinforcement of elastomers by colloidal nanoparticles is an important application where microstructure needs to be understood - and if possible controlled - if one wishes to tune macroscopic mechanical properties. Here the three-dimensional structure of big aggregates of nanometric silica particles embedded in a soft polymeric matrix is determined by Small Angle Neutron Scattering. Experimentally, the crowded environment leading to strong reinforcement induces a strong interaction between aggregates, which generates a prominent interaction peak in the scattering. We propose to analyze the total signal by means of a decomposition in a classical colloidal structure factor describing aggregate interaction and an aggregate form factor determined by a Reverse Monte Carlo technique. The result gives new insights in the shape of aggregates and their complex interaction in elastomers. For comparison, fractal models for aggregate scattering are also discussed.