The curved surface of a frustum is cut open and laid flat. The two CURVED edges of the flat shape have lengths equal to:

Flattening the curved surface gives an annular sector; its outer and inner arcs are exactly the two rims opened out, so their lengths are $2\pi R$ and $2\pi r$ - the circumferences. The straight edges of the flat shape are the slant height. This is why CSA can also be written $\frac{1}{2}(\text{sum of the two circumferences})\times l$.