A quadrangular pyramid, the base is a counter rectangle with sides 15 and 20 cm.

A quadrangular pyramid, the base is a counter rectangle with sides 15 and 20 cm. The side edges are 25 cm. Find the height of the pyramid.

The height of the pyramid passes through the intersection of the diagonals of the rectangle. Find the diagonal by the Pythagorean theorem:
d = √ (a² + b²) = √ (225 + 400) = √625 = 25 (cm).
Consider a right-angled triangle in which the leg (half of the diagonal – d / 2), the hypotenuse (side edge of the pyramid – L) are known, and we need to find the second leg (the height of the pyramid – H).
H = √ (L² – (d / 2) ²) = √ (625 – 625/4) = √ (1875/4) = 25√3 / 2 = 21.6506336 ≈ 21.65 (cm).
Answer: The height of the pyramid is 21.65 cm.