In a rectangular parallelepiped, the lengths of the sides are 10, 15, 20 cm, find the area of the diagonal section.

Let’s draw a diagonal AC at the base of the parallelepiped.

Since the parallelepiped is rectangular, the AСD triangle is rectangular.

By the Pythagorean theorem, we determine the length of the hypotenuse AC.

AC ^ 2 = AD ^ 2 + СD ^ 2 = 15 ^ 2 + 10 ^ 2 = 225 + 100 = 325.

AC = 5 * √13 cm.

The diagonal section is a rectangle АА1С1С, then its area is equal to:

Ssection = АС * АА1 = 5 * √13 * 20 = 100 * √13 cm2.

If the height is 10 cm, then AC = √400 + 225 = √625 = 25 cm.

Ssection = 25 * 10 = 250 cm2.

If the height is 15 cm, then AC = √400 + 100 = √500 = 10 * √5 cm.

Ssection = 10 * √5 * 15 = 150 * √5 cm2.

Answer: The area of ​​the diagonal section can be 100 * √13 cm2, 250 cm2, 150 * √5 cm2.