# 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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