Finding side length of a cross-section of a pyramid frustum/truncated pyramid

Question

How do I find the side length of a cross-section (as illustrated in the drawing below - cross-section in red) of a pyramid frustum/truncated pyramid?

I know the side-lengths of the top and bottom base, the height of the frustum and the distance to the cross-section. Furthermore I know the top and bottom base are parallel and that the center of the top and bottom base are directly on top of each other.

Answer 1

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).