In the pyramid, the base area is 150 cm2, the parallel cross-sectional area is 54 cm2, the distance

In the pyramid, the base area is 150 cm2, the parallel cross-sectional area is 54 cm2, the distance between them is 14 cm. Determine the height of the pyramid.

A section parallel to the base cuts off from the ABCS pyramid a similar A1B1C1S pyramid with a similarity coefficient equal to the square root of the area ratio.

K = √S / S1 = √150 / 54 = √25 / 9 = 5/3.

Let’s denote the height of the OS of the pyramid through X, then O1S = (X – 14).

Then:

X / (X – 14) = 5/3.

5 * X – 70 = 3 * X.

2 * X = 70.

X = 70/2 = 35 cm.

Answer: The height of the pyramid is 35 cm.