Ok, so:
We have to find the area of a sector of a circle. A sector is the region bounded by a central angle and its intercepted arc, such as the shaded region.
Let me draw the situation:
We want to find the shaded area ( Blue ).
For this, there's an equation which could be really useful. This is:
In a circle of radius r, the area A of the sector inside a central angle θ is:
A = (1/2) r²θ.
Where r is the radius and θ is the angle measured in radians!.
We got the angle measured in degrees, so we have to convert it to radians.
Now, we can replace in the equation:
A = (1/2) r²θ.
We know that r = 6 and θ = (2π)/3.
A = (1/2) (6)²(2π)/3.
A = (1/2) (36)(2π)/3.
Simplifying:
A = 12π, which is approximately: 37.6991.
If we round to the nearest hundredth; this is: 37.70
