The four-cornered peramid, the base area is 150 cm2, the area of the parallel section is 54 cm2, the distance

The four-cornered peramid, the base area is 150 cm2, the area of the parallel section is 54 cm2, the distance between the base and the section of 14 cm will determine the height of the pyramid.

The height of the main pyramid “S = x + 14”
Height of the upper pyramid from the parallel base “x”
Using the formula for the volume of a pyramid and a truncated pyramid, we define a system of equations that will allow us to find the desired one:
1/3 * (x + 14) * 150 = 1/3 * 54x + 1/3 * 14 * (54 + 150 + √54 * √150)
(x + 14) * 150 = 54x + 14 * (54 + 150 + √54 * √150)
150x + 2100 = 54x + 2856 + 14 * √8100
150x-54x = 2856-2100 + 14 * 90
96x = 756 + 1260
96x = 2016
x = 21
So the height of the pyramid S = 21 + 14 = 35cm