In a regular quadrangular pyramid, height = 15, side edge SC = 25. Find the diagonal of the base

Let’s construct the diagonals AC and BM at the base of the pyramid.

The SOC triangle is rectangular, then by the Pythagorean theorem, we determine the length of the leg OC.

OC ^ 2 = SC ^ 2 – SO ^ 2 = 25 ^ 2 – 15 ^ 2 = 625 – 225 = 400.

OC = 20 cm.

Since the pyramid, by condition, is correct, there is a square at its base.

Point O is the middle of the diagonals of the square, then AC = ВD = OC * 2 = 20 * 2 = 40 cm.

Answer: The length of the diagonal of the base of the pyramid is 40 cm.