Answer
$$A=144-\frac{\pi d^2}{4}$$
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:
$$ A=12^2-\pi (\frac{d}{2})^2 \\ A=144-\frac{\pi d^2}{4}$$