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In the figure below, the diameters of two semicircles lie along the diameter of a larger semicircle. The two smaller semicircles are tangent to one another and the sum of the lengths of their diameters is equal to the length of the diameter of the larger semicircle. At the point where the two smaller semicircles are tangent, the height of the larger semicircle is 2 units.
Use this information to determine the area of the shaded region shown in the figure.
