Find the volume of a parallelepiped whose height is 6, the diagonal of the base is 13 cm, and one of the sides is 5.

It is known from the condition that the height of the parallelepiped is 6 cm, and it is also known that the diagonal of the base is 13 cm, and one of the sides of the base is 5 cm.

To calculate the volume of a rectangular parallelepiped, apply the formula:

V = a * b * c;

We know two quantities, we need to find the third. To do this, we will consider a right-angled triangle formed by the sides of the base and the diagonal of the rectangle. Let’s apply the Pythagorean theorem to find the unknown leg.

c ^ 2 = a ^ 2 + b ^ 2;

a = √ (c ^ 2 – b ^ 2) = √ (13 ^ 2 – 5 ^ 2) = √ (169 – 25) = √144 = 12 cm.

V = 6 * 5 * 12 = 30 * 12 = 360 cm ^ 3.