Hey n22.
Consider a flat surface.
I am confused as to what you mean here. Is "n" the unit normal to surface S and "k" the unit normal to surface A?
Apparently you are to find a surface, "A", so that the integral of over A is the same as the integral over S? What is "S"? Wouldn't it be simplest to take A= S?
And, since you have "=" between those two integrals, what does "explain why inequality holds" mean?