KöMaL 2016 C1363

The parallel sides of a right-angled trapezium are $405$ and $80$ units long. The length of the right-angled leg is $65 \big(\sqrt{3}+\sqrt{2}\,\big)$ units. The trapezium is sliced into eight trapezoids, all similar to one another, with cuts parallel to the bases. What is the height of the largest slice?