Find the volume of a rectangular parallelepiped, the sides of the base of which are 9

Find the volume of a rectangular parallelepiped, the sides of the base of which are 9 and 12 cm, the diagonal of the parallelepiped is 20 cm.

Determine the area of the base of the parallelepiped.

Sbn = AB * AD = 9 * 12 = 108 cm2.

From the right-angled triangle ABD, according to the Pythagorean theorem, we determine the length of the hypotenuse BD.

BD ^ 2 = AB ^ 2 + AD ^ 2 = 81 + 144 = 225.

ВD = 15 cm.

Determine, according to the Pythagorean theorem, the length of the leg BB1.

BB1 ^ 2 = DB1 ^ 2 – BD ^ 2 = 400 – 225 = 175.

BB1 = 5 * √7 cm.

Let’s define the volume of the parallelepiped.

V = Sbase * BB1 = 108 * 5 * √7 = 540 * √7 cm3.

Answer: The volume of a parallelepiped is 540 * √7 cm3.