Durability of an asphalt mixture is directly related to the optimum asphalt binder content, which guarantees coverage of the aggregate particles and suitable volumetric properties to ensure a good performance in service, producing an asphalt mixture that is less susceptible to aging and moisture damage. Previous research has shown that the polygon-of-voids tool, or polyvoids, is an analytical technique to determine the optimum asphalt binder content of asphalt mixtures with virgin aggregates based on the specification limits of voids, allowing a saving in time and material. However, current trends to develop new asphalt mixtures which incorporate reclaimed asphalt pavement (RAP) have created additional challenges given the nature of the design of a mixture containing aggregates with residual asphalt that make the property measurement of the bulk specific gravity of the RAP aggregate (G(sb)(RAP)) difficult. This paper aims to demonstrate the application of the polygon-of-voids tool for the design of recycled hot-mix asphalt. The results show that the method of substitution, where the value of the actual specific gravity of the (G(se)(RAP)) aggregate (CLAP) is assumed as the bulk specific gravity of the RAP aggregate (G(sb)(RAP)), gives the optimum asphalt contents closest to those determined by the traditional Marshall method for the design of asphalt mixtures.