The sides of the base of the rectangular parallelepiped are 7 and 24, and the height is 8, find the area of its diagonal section.

Let’s take for a and b the sides of the base of a rectangular parallelepiped, where a = 7, b = 24. Height h = 8.
The area of the diagonal section is:
S = d * h, where d is the diagonal of the base, is calculated from a triangle in which d is the hypotenuse, and a and b are legs. By the Pythagorean theorem:
d ^ 2 = a ^ 2 + b ^ 2;
d ^ 2 = 49 + 576;
d ^ 2 = 625;
d = 25.
In this way:
S = d * h = 25 * 8 = 200.
Answer: the area of the diagonal section is 200.