Grid Area Deducion

Does anyone know how to deduct areas of two overlapping grids (of its individual cells):

one base grid of particular shapes (squares) and overlay grid of the same shapes but with trimmed areas. Please see attached image.

What I am trying to do is to calculate areas of the black grid (under) and deduct all corresponding areas of overplayed grid (light blue grid). Main issue is that some times there are two pieces of the overlayed grid. 

Would anyone have any idea how to start?