Finding the side length of the cross section of a truncated cone / truncated pyramid pyramid

Question

How to find the lateral cross-sectional length (as shown in the figure below - cross-section in red) of the truncated / truncated pyramid?

alt text http://i30.tinypic.com/14adjx2.gif

I know the lateral lengths of the upper and lower bases, the height of the truncated cone and the distance to the cross section. In addition, I know that the upper and lower bases are parallel and that the center of the upper and lower lower bases is directly above each other.

Answer 1

The proportions are linear, so just interpolate the lengths of the lower and upper sides with a fraction of the cut height with the total height.

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

( , 100%).