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X = CD = 30

Shaded Rectangle Area = 70

Proof that R² = 2a² - b²

X = AC = 2.64575131106

Rectangle Area = 13.8564064606

Triangle ABC Side S = 12

X = DL = 19

Orange / Green = 100 / 81

Area DFH / Area BEG = 19 / 7

Shaded Area = 25 / 3