Final answer:
The area of the shaded region of the circle, after rounding to the nearest tenth, is approximately 140.0 m² given the provided radius and central angle.
Step-by-step explanation:
To calculate the area of the shaded region in the problem, we're dealing with a sector of a circle. The formula for the area of a sector is given by 0.5 * r² * θ, where r is the radius and θ is the central angle in radians.
In this case, the radius (r) is 11.1m and the angle (θ) is 130° or about 2.27 radians (since 1 radian ≈ 57.3°). So, plug these values into the formula and calculate the area:
A = 0.5 * (11.1m)² * 2.27 ≈ 139.4 m².
However, because the radius has only two significant figures, it limits the calculated area to two significant figures. Therefore, after rounding to the nearest tenth, the area of the shaded region is estimated to be 140.0 m².
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