In rectangular parallelepiped ABCDA1B1C1D1 the lengths of the edges are known: AB = 24; AD = 10;

In rectangular parallelepiped ABCDA1B1C1D1 the lengths of the edges are known: AB = 24; AD = 10; AA1 = 22. Find the area of the section through vertices A, A1, C.

The section plane passing through points A, A1 and C is a diagonal section that is a rectangle AA1C1C.
Consider a right-angled triangle ACB, in which the leg BC = AD = 10 cm, and the leg AB = 10 cm, then, according to the Pythagorean theorem, the hypotenuse of the AC will be equal to:
AC2 = AB2 + BC2 = 242 + 102 = 576 + 100 = 676.
AC = 26 cm.
Let’s define the sectional area АА1С1С.
S = AA1 * AC = 22 * 26 = 572 cm2.
Answer: The cross-sectional area is 572 cm2.