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To find the area of the blue shaded region in the circle, we need to calculate the area of the sector formed by the central angle of 130 degrees. Here’s how you can calculate it:

### Step-by-Step Calculation

1. **Identify the Given Values:**
   - Radius (\( r \)) of the circle: \( 11.1 \) meters
   - Central angle (\( \theta \)) of the sector: \( 130^\circ \)

2. **Formula for the Area of a Sector:**
   \[
   \text{Area of a Sector} = \pi r^2 \times \left(\frac{\theta}{360}\right)
   \]

3. **Substitute the Known Values into the Formula:**
   \[
   \text{Area} = \pi \times (11.1)^2 \times \left(\frac{130}{360}\right)
   \]

4. **Calculate the Squared Radius:**
   \[
   11.1^2 = 123.21 \text{ square meters}
   \]

5. **Calculate the Fraction of the Circle:**
   \[
   \frac{130}{360} \approx 0.3611
   \]

6. **Compute the Area:**
   \[
   \text{Area} = \pi \times 123.21 \times 0.3611 \approx 139.86 \text{ square meters}
   \]

7. **Round the Result to the Nearest Tenth:**
   \[
   \text{Area} \approx 139.9 \text{ square meters}
   \]

Therefore, the area of the blue shaded region is approximately **139.9 square meters**.

If you need further clarification or want to explore more about this topic, let me know! Here are some related questions that might interest you:

1. How do you derive the formula for the area of a sector?
2. What is the relationship between arc length and sector area?
3. How can you calculate the area of the remaining circle if you know the area of a sector?
4. How does changing the radius affect the area of a sector?
5. What is the significance of the central angle in determining the area of a sector?
6. How do you find the perimeter of a sector?
7. What other shapes can be formed using sectors?
8. How do angles in radians relate to angles in degrees?

### Tip

Always ensure your units are consistent when performing geometric calculations. If the radius is given in one unit, ensure all parts of your calculation use the same unit to maintain accuracy.

Learn how to calculate the area of the blue shaded region in a circle using a 130-degree central angle and a radius of 11.1 meters. This problem involves geometric calculations for the area of a sector, suitable for advanced high school students.

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