We have that the area of the sector of a circle can be found with the following equation:

where theta is the measure of the angle and r is the radius. In this case, we have the following:

then,using the formula for the area of a sector, we have:
![A=(60)/(360)(3.14)(6)^2=(2160)/(360)(3.14)=6\cdot3.14=18.84\operatorname{cm}^2]()
therefore, the area is 18.84 cm^2