The height of the cone is 12 and the generatrix 13 is to find the lateral surface of the cone.

The lateral surface area of the cone is calculated by the formula:

Sb = π R L, where:

Sb is the area of the lateral surface of the cone;

R is the radius of the base of the cone;

L – generatrix of the cone;

π – number ≈ 3.14.

In order to find the area of the lateral surface, you need to calculate the length of the radius of the base. To do this, we will use the generator formula:

L ^ 2 = R ^ 2 + H ^ 2, where:

L – generatrix of the cone;

R is the radius of the base;

H is the height.

R ^ 2 = L ^ 2 – H ^ 2;

R ^ 2 = 13 ^ 2 – 12 ^ 2 = 169 – 144 = 25;

R = √25 = 5 cm.

Sb = 3.14 * 5 * 13 = 204.1 cm2.

Answer: the area of the lateral surface of the cone is 204.1 cm2.