Find the area of the diagonal section of a rectangular parallelepiped whose height is 12cm

Find the area of the diagonal section of a rectangular parallelepiped whose height is 12cm, and the sides of the base are 8cm and 6cm.

The diagonal section of a rectangular parallelepiped is a rectangle, one of the sides of which is equal to the height of the parallelepiped, the other is the diagonal of the base.

Knowing the sides of the base, we can find the diagonal by the Pythagorean theorem:

d ^ 2 = 6 ^ 2 + 8 ^ 2 = 36 + 64 = 100 = 10 ^ 2;

d = 10 cm.

The area of the diagonal section is equal to the product of the diagonal of the base and the height of the parallelepiped:

Ssection = h * d = 12 * 10 = 120 cm2.