To find the area of a sector in a circle, the formula involves multiplying the fraction of the circle represented by the angle by the area of the entire circle. In this case, the angle of 270 degrees simplifies to 3/4 when divided by 360 degrees. The area \(A\) is calculated as \(A = \frac{3}{4}\pi r^2\). With a radius of 12 meters, substituting into the formula gives an area of 108π. The final answer of 108π is confirmed as correct.