Through the generatrix of the cylinder, two mutually perpendicular sections are drawn

Through the generatrix of the cylinder, two mutually perpendicular sections are drawn, the areas of which are 10 and 24. find the area of the axial section.

It is known that perpendicular sections form right-angled triangles on the bases of the cylinder.
Thus, we can designate legs a and b. You also know that the diagonal is the base diameter D. The height of the cylinder Н.
Having all the data, we can find Sо:
So = H * D;
So = H * √ (a² + b²);
So = H * √ ((10 / H) ² + (24 / H) ²).
So = √ (100 + 576);
So = √676;
So = 26.
Answer: So = 26.