The height of a regular quadrangular pyramid is 16 cm, the side of its base is 24 cm.

The height of a regular quadrangular pyramid is 16 cm, the side of its base is 24 cm. Calculate the distance from the top of the pyramid to the top of the base.

Let’s draw diagonals at the base of the pyramid.

Since the pyramid is correct, there is a square at its base. The diagonal of the square is:

AC = a * √2, where a is the length of the side of the square.

AC = AD * √2 = 24 * √2 cm.

The diagonals of the square, at the intersection point, are divided in half, then AO1 = AC / 2 = 24 * √2 / 2 = 12 * √2 cm.

In a right-angled triangle OO1A, the hypotenuse OA is the distance from the top of the pyramid to the top of the base.

OA ^ 2 = O1A ^ 2 + OO1 ^ 2 = (12 * √2) ^ 2 + 16 ^ 2 = 288 + 256 = 544.

ОА = √544 = 4 * √34 cm.

Answer: ОА = 4 * √34 cm.