I do PacMan because I
PacMan. Ignore the eye of PacMan because we will just subtract that off the answer. Now the angle the circle makes from $\displaystyle (3,-3)$ to $\displaystyle (3,3)$ so from $\displaystyle -\frac{\pi}{4}$ to $\displaystyle \frac{\pi}{4}$. The equation of the circle in polar coordinates is simply $\displaystyle r$. In this case the radius is $\displaystyle r=2\sqrt{3}$. So the mouth of PacMan is described in area by:
$\displaystyle \frac{1}{2}\int_{-\pi/4}^{\pi/4} (2\sqrt{3})^2 d\theta$.
Once you know the mouth of PacMan you can subtract the total area of his mouth to get his body. And then subtract PacMan's eye to get your answer.