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 \(a+b+c\).