The area of the circle is 27π square units.
The formula to find the area of a circle is A = πr², where A represents the area and r represents the radius.
In this case, the radius DB is 6 meters and the angle ∠ADB is 120°.
To find the area of the circle, we need to find the value of r.
To do this, we can use the trigonometric relationship of a triangle and the given angle:
sine(∠ADB) = height / radius
sin(120°) = height / 6
height = sin(120°) × 6
height = (√3/2) × 6 = 3√3
Now, we can use the height as the radius to calculate the area:
A = π(3√3)² = 9π√3² = 9π × 3 = 27π
So, the area of the circle is 27π square units.