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To find the perimeter of the shaded region, we need to analyze the figure in more detail.

The figure shows four arcs centered at the vertices \( A, B, C, \) and \( D \) of a square with side length 4. Each arc is a quarter circle with a radius equal to the side length of the square, which is 4.

First, we need to find the lengths of the arcs that make up the perimeter of the shaded region. Each shaded region is bounded by parts of these arcs.

The perimeter of the shaded region can be determined as follows:

1. The total length of one quarter circle with radius 4 is given by:
   \[
   \text{Length of one arc} = \frac{1}{4} \times 2\pi \times 4 = 2\pi
   \]

2. Each arc that contributes to the perimeter of the shaded region is a segment of a circle.

Since the shaded region's perimeter consists of four such arc segments from each corner, the total perimeter \( P \) is given by:
   \[
   P = 4 \times 2\pi = 8\pi
   \]

3. Converting \( 8\pi \) to a numerical value:
   \[
   8\pi \approx 8 \times 3.1416 \approx 25.1
   \]

Thus, the perimeter of the shaded region, rounded to one decimal place, is approximately 25.1 units.

So the answer is not among the given options, indicating there might be an error in the question or the provided choices. However, based on the calculation, the perimeter is:

\[ \boxed{25.1} \]

Would you like to go over the details again or have any further questions?

Here are 5 questions you might want to ask next:

1. How can we verify if our calculations for the perimeter are correct?
2. What are some common mistakes to watch out for when solving problems involving arcs?
3. Can you explain how to find the area of the shaded region instead of the perimeter?
4. How would the problem change if the side of the square were different?
5. What are some real-life applications of finding perimeters of composite figures?

**Tip:** When dealing with geometry problems involving circles and arcs, always consider the relationship between the radius, diameter, and the proportion of the circle being used.

Learn how to calculate the perimeter of a shaded region formed by arcs in a square geometry problem. Detailed step-by-step solution involving quarter circles and radius analysis. Suitable for students in Grades 10-12.

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