Area Of A Sickle

Geometry Level 3

In the above diagram, each of the grid squares is a unit long. Also, all the arcs are quadrants. If the area of the shape enclosed by arcs $DB$ , $BJ$ , $JK$ , and $KD$ can be represented as $\dfrac{a \pi + b}{c},$ where $a,b,c$ are integers with $c$ positive, find the maximum value of $a+b+c$ .