Answer
$$A=z^2-36\pi$$
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:
$$ A=z^2-\pi (\frac{12}{2})^2 \\ A=z^2-36\pi$$
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