# 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.

September 29, 2021 | education

| 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.

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