Answer: [tex]12\pi[/tex] square units
Step-by-step explanation:
Area of sector is given by :
[tex]A=\dfrac{x}{360^{\circ}}\pi r^2[/tex] , where x is the central angle made by arc and r is the radius of the circle .
As per given , we have
[tex]x=120^{\circ}[/tex]
Radius = 6 units
Then, the area of the sector made by arc will be :
[tex]A=\dfrac{120^{\circ}}{360^{\circ}}\pi (6)^2\\\\=\dfrac{1}{3}\pi (36)=12\pi[/tex]
Hence, the area of the sector of the circle formed by this central angle = [tex]12\pi[/tex] square units.
