The formula for the lateral area of ​​a cone is:

Suppose the base radius of the cone is r, the height is h, and the generatrix length is l (l^=r^+h^).

The side view of a cone is a sector with a radius of l and an arc length of 2πr.

∴The lateral area of ​​the cone = (1/2)(2πr)l = πrl