Area calculating part 3

Geometry Level 3

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

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