In this talk we present an explicit area formula to compute the spherical Hausdorff measure of an intrinsic regular graph in an arbitrary homogeneous group. We assume the intrinsic graph to be intrinsically differentiable at any point with continuous intrinsic differential. The key aspect of the result lies in the introduction of a suitable notion of intrinsic Jacobian and in the computation of an explicit expression for this object. Eventually, we present recent results about the symmetries of some homogeneous distances for which the area formula takes a simplified expression. This is a joint work with V. Magnani (Unipi). Attività di ricerca supportata dal progetto INDAM-GNAMPA-2024: "Free boundary problems in noncommutative structures and degenerate operators" CUP E53C23001670001