The height of the cone is 5 and the length of the generatrix is 13, find the axial sectional area of this cone.

The height of the cone (h) forming (l) and R of the base form a right-angled triangle. We find R bases by the Pythagorean theorem: R ^ 2 = l ^ 2-h ^ 2 = 169-25 = 144 => R = 12
The axial sectional area (S) is equal to a triangle with sides l and base 2R. Find the area of a right-angled triangle S1 = 12 * 5/2 = 30, hence the area of the axial section S = 2S1 = 60.
Answer: the area of the axial section of the cone will be equal to 60