smc

The wanted area can be divided into a semicircle and a circular segment. The area of the semicircle is $\frac{1}{2}\cdot \pi \cdot 6^2=18\pi$ square feet. To find the area of the circular segment, note that by using 30-60-90 triangles (or Law of Cosines), the chord's length is $6\sqrt{3}$ ft, and the angle of the sector is $120^{\circ }$. That means the area of the circular segment is $(\frac{1}{3}\cdot \pi \cdot 6^2)-(\frac{1}{2}\cdot 6\sqrt{3}\cdot 3)=12\pi -9\sqrt{3}$ square feet. Thus, the area of the remaining grassy area is $\boxed{30\pi -9\sqrt{3}}$ square feet.