In the figure below is a rectangle with and . Point lies , point lies on , and is a right angle. The areas of and are equal. What is the area of ?

Note: On certain tests that took place in China, the problem asked for the area of .
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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site. Also appeared as 2024 12B #7.