GCSE Maths non-calc

Hello, this was the last question on my GCSE Maths Non-calculator on thursday.

Angle C is 90 degrees

AC=BC

If the area of the shaded region in $\text{cm}^2$ can be written as $\dfrac{a - \sqrt{b}}{c}$ where $a, b, c$ are positive integers and $b$ is squarefree, find $a + b + c$ .