  We consider submanifolds of sub-Riemannian Carnot groups with intrinsic $C^1$
regularity ($C^1_H$). Our first main result is an area formula for $C^1_H$
intrinsic graphs; as an application, we deduce density properties for Hausdorff
measures on rectifiable sets. Our second main result is a coarea formula for
slicing $C^1_H$ submanifolds into level sets of a $C^1_H$ function.
