$A(-1,1)$, $B$, and $C$ are points on the hyperbola $x^2 - y^2 = 1$. If $\triangle ABC$ is a regular triangle, find the area of $\triangle ABC$. The original answer is in the form of k\sqrt{m}, please give the value of k + m.

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