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Jack and Elsa are in the process of shoveling their driveway which is 12 feet wide and 24 feet long. Using two different sized shovels, each of them began in one corner and proceeded to clear a straight path to the opposing corner. Their paths are shown in the figure below.
Determine the area of the region in the driveway where their paths overlapped (the shaded region in the figure). You must include sufficient work to support your answer.
