Answer:
Option (B)
Step-by-step explanation:
Area of sector of a circle = [tex]\frac{\theta}{360}(\pi r^{2} )[/tex]
where r = radius of the circle
θ is the central angle subtended by the arc TS.
Area of the given sector = [tex]\frac{120}{360}(\pi) (24^{2} )[/tex]
= [tex]\frac{576\pi }{3}[/tex]
= 192π
= 603.19 unit²
Area of the triangle (not shaded) = [tex]\frac{1}{2}(\text{TC})(\text{CS})\text{sin}(120)[/tex]
= [tex]\frac{1}{2}(24)(24)(\text{sin}120)[/tex]
= 167.22 unit²
Area of the shaded area = Area of the sector - Area of triangle
= 603.19 - 167.22
= 435.96 unit²
Therefore, the area of the shaded region = 435.96 unit²
The nearest value of the area has been given in Option (B).
So Option B will be the answer.
