Area calculating part 3

Geometry Level 3

ABCD ABCD is a rectangle with sides AB=2 AB = 2 and BC=1 BC = 1 . EF EF is a circular arc with point B B as its centre. Also, point E E is a midpoint of the segment CD CD . If the green region can be represented as 1a(bπ) \frac{1}{a}(b - \pi) , where a a and b b are both positive integers, find the value of a+b a + b

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