Find the area of the shaded sector 12 and 1000 degrees?

To find the area of a shaded sector, use the formula:

[ \text{Area} = \frac{\theta}{360} \times \pi r^2 ]

where (\theta) is the angle in degrees and (r) is the radius. In this case, with a radius of 12 and an angle of 1000 degrees, first reduce the angle by finding its equivalent angle within a full circle (1000 mod 360 = 280 degrees). Then, plug the values into the formula:

[ \text{Area} = \frac{280}{360} \times \pi \times 12^2 \approx 235.62 \text{ square units}. ]