A region is bounded by semicircular arcs constructed on the side of a square whose sides measure $\frac{2}{\pi}$, as shown. What is the perimeter of this region?
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$\textbf{(A) } \frac{4}{\pi}\qquad \textbf{(B) } 2\qquad \textbf{(C) } \frac{8}{\pi}\qquad \textbf{(D) } 4\qquad \textbf{(E) } \frac{16}{\pi}$
Since the side of the square is the diameter of the semicircle, the radius of the semicircle is $\frac{1}{2}\cdot\frac{2}{\pi}=\frac{1}{\pi}$.
Since the length of one of the semicircular [arcs](https://artofproblemsolving.com/wiki/index.php/Arc) is half the circumference of the corresponding circle, the length of one arc is $\frac{1}{2}\cdot2\cdot\pi\cdot\frac{1}{\pi}=1$. 
Since the desired perimeter is made up of four of these arcs, the perimeter is $4\cdot1=\boxed{\textbf{(D) }4}$.