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Cos alpha = 3 / 5 = 0.6

X = BCE = 21

Orange Area = 8

X = CD = 6

X = Angle CBD = 10

Shaded Area = 13 / 18

Another Approach

New / Simplified

Green / Purple = 1.2 = 6 / 5

X = ABD = 24

Circle Area = 79.4142289853

Triangle Height BC = 6