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 to so from to . The equation of the circle in polar coordinates is simply . In this case the radius is . So the mouth of PacMan is described in area by:
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.