A region is bounded by semicircular arcs constructed on the side of a square whose sides measure $ 2/\pi $, as shown. What is the perimeter of this region? 

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$ \textbf{(A) }\frac {4}\pi\qquad\textbf{(B) }2\qquad\textbf{(C) }\frac {8}\pi\qquad\textbf{(D) }4\qquad\textbf{(E) }\frac{16}{\pi} $
1. **Identify the shape and dimensions:**
   - The problem involves a square with side length \( \frac{2}{\pi} \).
   - Semicircular arcs are constructed on each side of the square.

2. **Determine the radius of the semicircles:**
   - The diameter of each semicircle is equal to the side length of the square, which is \( \frac{2}{\pi} \).
   - Therefore, the radius \( r \) of each semicircle is:
     \[
     r = \frac{\text{diameter}}{2} = \frac{\frac{2}{\pi}}{2} = \frac{1}{\pi}
     \]

3. **Calculate the circumference of a full circle with this radius:**
   - The circumference \( C \) of a full circle with radius \( \frac{1}{\pi} \) is given by:
     \[
     C = 2\pi \times \frac{1}{\pi} = 2
     \]

4. **Calculate the circumference of a semicircle:**
   - Since a semicircle is half of a full circle, the circumference of one semicircle is:
     \[
     \frac{C}{2} = \frac{2}{2} = 1
     \]

5. **Sum the circumferences of all four semicircles:**
   - There are four semicircles, each with a circumference of 1. Therefore, the total perimeter \( P \) of the region is:
     \[
     P = 1 + 1 + 1 + 1 = 4
     \]

Conclusion:
\[
\boxed{4}
\]