abstract: Motivated by a visual perception problem, we consider a notion of area for submanifolds of given degree in a Carnot manifold endowed with a Riemannian metric. Particular cases are the length of geodesics in sub-Riemannian manifolds and the perimeter of hypersurfaces in contact sub-Riemannian manifolds. Among others, we consider the relation with the spherical Hausdorff measure associated to the Carnot-Carathéodory distance, the problem of integrability of deformations, the notion of regular submanifolds, and the first variation formula. This is joint work with Gianmarco Giovannardi and Giovanna Citti.