Following the previous puzzles and the relationships between lengths of a right trapezium with an inscribed circle, if we were to follow that through to equations I believe we would end up with quartic equations awkward to work with.

More practically in this instance we can just use trial and error, and very quickly find that each trapezoid as we descend the figure is 50% bigger than the one above. So the horizontal lines measure 40, 60, 90 and 135. The sloping lines will then be 51, 78 and 117. And the vertical lines will be 48, 72 and 108, giving the overall height of 228.