The height of a regular quadrangular pyramid is 3 cm, the side of the base is 4 cm. Find the length of the side of the rib.

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 = 4 * √2 cm.

The diagonals of the square, at the intersection point, are divided in half, then AO1 = AC / 2 = 4 * √2 / 2 = = 2 * √2 cm.

In the right-angled triangle OO1A, the hypotenuse OA is the lateral edge of the pyramid.

OA ^ 2 = O1A ^ 2 + OO1 ^ 2 = (2 * √2) ^ 2 + 3 ^ 2 = 8 + 9 = 17.

ОА = √17 cm.

Answer: The length of the side ribs of the pyramid is √17 cm.