Semicircle inscribed in a square

Geometry Level 4

Let $ABCD$ be a unit square. What is the area of the largest semicircle that can be inscribed inside it?

If your answer is of the form $(a-b\sqrt{c})\pi$ , where $a$ , $b$ and $c$ are integers and $c$ is square-free, write your answer as $a+b+c$ .