Let \(\omega=-\tfrac{1}{2}+\tfrac{1}{2}i\sqrt{3}.\) Let \(S\) denote all points in the complex plane of the form \(a+b\omega+c\omega^2,\) where \(0\leq a \leq 1,0\leq b\leq 1,\) and \(0\leq c\leq 1.\) Find the area of \(S.\) The original answer is in the form \(\frac{k}{m}\sqrt{n}\), please give the value of k + m + n.

Let's think step by step and output the final answer within \boxed{}.
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