+7  A: 

The proportions are linear, so just interpolate the lengths of the bottom and top sides with the proportion of the cut height with the total height.

cut_side = (cut_height/total_height)*(bottom_side-top_side)+top_side

(Anyway, double check it to be 100% sure).

fortran
alternatively: alpha*top_side + (1-alpha)*bottom_side, where alpha = cut height / total height
Jason S