Problem
2006 AMC 10B Problem 6
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?
![[asy] unitsize(1cm); defaultpen(.8); filldraw( circle( (0,1), 1 ), lightgray, black ); filldraw( circle( (0,-1), 1 ), lightgray, black ); filldraw( circle( (1,0), 1 ), lightgray, black ); filldraw( circle( (-1,0), 1 ), lightgray, black ); filldraw( (-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle, lightgray, black ); [/asy]](/static/aops/7b38113c08d3a31597444d88c0f64f603a6e8c33.png)
\mathrm{(A) \ } \frac{4}{\pi}\qquad \mathrm{(B) \ } 2\qquad \mathrm{(C) \ } \frac{8}{\pi}\qquad \mathrm{(D) \ } 4\qquad \mathrm{(E) \ } \frac{16}{\pi}
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