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We are given a square containing a circle, and we need to find the area of the shaded region. 

### Step-by-step solution:

1. **Area of the square**:
   - The side length of the square is 10 meters (since it matches the diameter of the circle).
   - The area of the square is:
   \[
   A_{\text{square}} = 10 \times 10 = 100 \text{ square meters}
   \]

2. **Area of the circle**:
   - The radius of the circle is 5 meters.
   - Using \( \pi \approx 3.14 \), the area of the circle is:
   \[
   A_{\text{circle}} = \pi \times r^2 = 3.14 \times 5^2 = 3.14 \times 25 = 78.5 \text{ square meters}
   \]

3. **Area of the shaded region**:
   - The shaded region is the area of the square minus the area of the circle:
   \[
   A_{\text{shaded}} = A_{\text{square}} - A_{\text{circle}} = 100 - 78.5 = 21.5 \text{ square meters}
   \]

Thus, the closest area of the shaded region is **21.5 square meters**, which corresponds to the first option.

Would you like more details on any part of this solution?

### Related Questions:
1. How do you derive the formula for the area of a circle?
2. What would the shaded area be if the radius of the circle were doubled?
3. How does changing the value of \( \pi \) affect the result?
4. What is the formula for finding the area of a sector in a circle?
5. How does the relationship between a square and an inscribed circle work geometrically?

### Tip:
Always ensure you correctly identify the radius or diameter when working with circle-related problems to avoid common mistakes!

Which is the closest to the area of the shaded region in the given square containing a circle?

Find the closest value to the shaded area of a square containing a circle. The square has a side length of 10 meters, and the circle has a radius of 5 meters. The solution involves subtracting the area of the circle from the area of the square. This problem is ideal for Grades 6-8 and involves key geometric concepts.

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