解：大圆的直径为$a+2b，$因此半径为$\frac {a+ 2b}2$
面积为：$ S_{大圆} = \pi (\frac {a+ 2b}2 )^2 = \pi (\frac {a^2 + 4ab + 4b^2}4 ) = \frac {\pi (a^2 + 4ab + 4b^2)}4 $
三个小圆的直径分别为$a、$$b、$$b$
因此半径分别为$\frac {a}2、$$\frac {b}2、$$\frac {b}2$
面积分别为：$ S_{小圆1} = \pi (\frac {a}2 )^2 = \frac {\pi a^2}4，$$S_{小圆2} = \pi (\frac {b}2 )^2 = \frac {\pi b^2}4 $
$S_{小圆3} = \pi (\frac {b}2 )^2 = \frac {\pi b^2}4 $
三个小圆的总面积为：$ S_{小圆总} = \frac {\pi a^2}4 + \frac {\pi b^2}4 + \frac {\pi b^2}4 = \frac {\pi (a^2 + 2b^2)}4 $
∴$S_{剩下} = S_{大圆} - S_{小圆总} $
$= \frac {\pi (a^2 + 4ab + 4b^2)}4 - \frac {\pi (a^2 + 2b^2)}4 = \frac {\pi ( 4ab + 2b^2)}4 $
