Answer
$$A=.25\pi x^2 -6$$
Work Step by Step
We know the following equation for the area of the shaded region:
$$ A_{shaded}=\text{Overall Area} - \text{ Area Used Up}$$
Using this, we find:
$$ A=\pi (\frac{x}{2})^2-(2)(3) \\ A=.25\pi x^2 -6$$