In a regular quadrangular pyramid, the diagonal of the base is 10, and the side edge is 13. Find the volume of the pyramid.

At the base of a regular pyramid is a square, then its diagonals, at the point of their intersection, are divided in half. OA = OC = AC / 2 = 10/2 = 5 cm. From the right-angled triangle KOС, according to the Pythagorean theorem, we define the leg KO, which is the height of the pyramid.

KO ^ 2 = KC ^ 2 – OC ^ 2 = 169 – 25 = 144.

KO = 12 cm.

The base area of a square is half the products of its diagonals.

Sbn = АС ^ 2/2 = 100/2 = 50 cm2.

Then the volume of the pyramid is: V = Sosn * KO = 50 * 12 = 600 cm3.

Answer: The volume of the pyramid is 600 cm3.