To find the area of the sector we will use
[tex]A=\frac{L\cdot r}{2}[/tex]
Where L is
[tex]\begin{gathered} L=\frac{2\cdot\pi\cdot6\text{ km}}{360^{\circ}}\cdot132^{\circ} \\ L=\frac{132\pi\text{ km}}{30}=\frac{66\pi\text{ km}}{15}=\frac{22\pi\text{ km}}{5} \end{gathered}[/tex]
Finally, we must replace L and r in the intial equation
[tex]A=\frac{\frac{22\pi\text{ km}}{5}\cdot6\operatorname{km}}{2}=\frac{\frac{132\pi\text{ km2}}{5}}{2}=\frac{132\pi\text{ km2}}{10}=\frac{66\pi}{5}km^2[/tex]
