The height of a regular quadrangular pyramid is 12cm, and the side of the base is 5√2cm.

The height of a regular quadrangular pyramid is 12cm, and the side of the base is 5√2cm. Find the side edge of the pyramid.

Since the pyramid is correct, there is a square at its base. Then in a right-angled triangle ABC, by the Pythagorean theorem, we determine the length of the hypotenuse AC.

AC ^ 2 = AB ^ 2 + BC ^ 2 = 2 * AB ^ 2 = 2 * (5 * √2) ^ 2 = 100.

AC = 10 cm.

In the square, the diagonals, at the point of their intersection, are divided in half, then AO = CO = AC / 2 = 10/2 = 5 cm.

From the right-angled triangle PAO, we determine, by the Pythagorean theorem, the length of the hypotenuse AP.

AP ^ 2 = PO ^ 2 + AO ^ 2 = 144 + 25 = 169.

AP = 13 cm.

Answer: The length of the side edge of the pyramid is 13 cm