  We consider surface area approximations by Lagrange and Crouzeix--Raviart
interpolations on triangulations. For Lagrange interpolation, we give an
alternative proof for Young's classical result that claims the areas of
inscribed polygonal surfaces converge to the area of the original surface under
the maximum angle condition on the triangulation. For Crouzeix--Raviart
interpolation we show that the approximated surface areas converge to the area
of the original surface without any geometric conditions on the triangulation.
