It is easy to obtain the new surfaces by using geometry.split to cut the grey area from light blue rectangle as the image on the left-hand side.
However, is there any way to cut away the non-intersected portion as well and obtain the surface as the black area on the right-hand side?
Assuming you have linear surfaces:
Get the UV parameter at point for all points which made up each of the subtracted surfaces.
Get the relevant U (or V it depends on how your surface is oriented) values.
Drop an duplicate values for each sublist and sort.
Draw isocurves on the new surface using an isocurve at parameter node.
Get the area of each.
