What is the exact area of the shaded region for the given circle with a central angle of 120° and a radius of 6?

We know that

[area of a circle]=pi*r²
for radius r=6 units
[area of a circle]=pi*6²> 36*pi unit²

the shaded region has a central angle of (360°-120°)> 240°
so

if 360° (full circle)  has an area of> 36*pi units²
 240° (shaded region)> X
X=240*36*pi/360> x=24*pi units²

the answer is
24*pi units²

The mode of the numbers is 29.