To find the area of a shaded sector of a circle, you can use the following formula:
\[ \text{Area of Sector} = \frac{\theta}{360} \times \pi r^2 \]
where:
- \(\theta\) is the angle of the sector in degrees,
- \(r\) is the radius of the circle.
For your question:
- \(\theta = 110^\circ\)
- \(r = 28 , \text{m}\)
Now, substitute these values into the formula:
\[ \text{Area of Sector} = \frac{110}{360} \times \pi (28)^2 \]
Calculating \(28^2\):
\[ 28^2 = 784 \]
Now substituting that into the area calculation:
\[ \text{Area of Sector} = \frac{110}{360} \times \pi \times 784 \]
Calculating \(\frac{110}{360}\):
\[ \frac{110}{360} = \frac{11}{36} \]
Now substituting back into the equation:
\[ \text{Area of Sector} = \frac{11}{36} \times \pi \times 784 \]
Calculating \(\frac{11 \times 784}{36}\):
\[ 11 \times 784 = 8624 \]
Now, divide this by \(36\):
\[ \frac{8624}{36} \approx 239.0 \]
Finally, multiply by \(\pi\) (approximately \(3.14159\)):
\[ \text{Area of Sector} \approx 239.0 \times 3.14159 \approx 751.39 , \text{m}^2 \]
Thus, the area of the shaded sector is:
\[ \text{Area of the shaded sector} \approx 751.39 , \text{m}^2 \]
You can round it to a suitable number of significant figures as per your requirement. The final answer is approximately:
\[ 751.39 , \text{m}^2 \]