Statistical properties of traces of fracture networks are related to the fracture volumetric density and to the average fracture surface and perimeter. These relations which hold whatever the fracture shapes provided that they are convex, can be extended to anisotropic networks. These relations can be used to check the statistical consistency of field data and to obtain macroscopic quantities such as the dimensionless density ρ' which controls the geometric and transport properties of fractured media. A field example of anisotropic subvertical fractures whose sizes obey a power law, is analyzed along these lines.