Find the area of the shaded region in the figure Find the area of the shaded region in the figure



What steps should I do? I tried following the steps listed here https://answers.yahoo.com/question/index?qid=20100305030526AAef8nZ

But I got 150.7 which is wrong.
Hint: Break the shaded region up into two shapes. One is a portion of the circle (you know the portion because of the given angle), and the other is a triangle (which is equilateral). Find the area of each shape and then add them.
Notice, the area of the equilateral triangle (indicated by red) $$=\frac{1}{2}(12)(12)\sin\frac{\pi}{3}$$ $$=72\frac{\sqrt{3}}{2}= 36\sqrt{3}$$  The area of the major circular sector subtending at the center an angle $2\pi-\frac{\pi}{3}=\frac{5\pi}{3}$ $$=\frac{1}{2}\left(\frac{5\pi}{3}\right)(12)^2=120\pi$$ Hence, the area of the shaded portion $$=\text{area of (red) triangle}+\text{area of major sector}$$ $$=\color{blue}{36\sqrt{3}+120\pi\approx 439.34494 \ }$$