11. (12 points) The figure is composed of an equilateral triangle and a regular hexagon. If the area of the equilateral triangle is 960, and the area of the regular hexagon is 840, then the area of the shaded part is $\qquad$ .
【Solution】The area of the middle triangle is $840 \div 2=420$. According to the bird head model, it can be calculated that $A$ is a quarter point. The area of triangle $B O E$ is $\frac{1}{6}$ of the hexagon's area, which is $840 \div 6=140$. The area of triangle $B O C$ is $960 \div 4-140=100$;
$C B: B E: E D=5: 7: 4$, the area of triangle $A B C$ is $960 \times \frac{5}{16} \times \frac{1}{4}=75$
Thus, the area of the shaded part is $960-75 \times 3=735$