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A diameter of circle $A$ is $12$ cm. If the measure of $ \angle BAC $ is $ { 120 }^{ \circ } $, as is shown in the diagram above, then what is the area of the shaded segment of circle $A$ ?

$ 6\pi -9\sqrt { 3 } $

$ 12\pi -9\sqrt { 3 } $

$ 12\pi -4.5\sqrt { 3 } $

$ 12\pi -18\sqrt { 3 } $