The parabolas $y^2 = 3x$ and $y^2 = -3x$ each intersect the circle $x^2 + y^2 = 4$ at two points, giving four points of intersection total.  Find the area of the quadrilateral whose vertices are these four points.The answer is in the form k\sqrt{m}+n,. Please provide the value of k + m + n.

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