Answer:
4
Step-by-step explanation:
The perimeter of the region is equal to the sum of the perimeter of the four semicircular arc. Since the semicircular arcs have the same measure, therefore:
Perimeter of region = 4 × Perimeter of semicircular arc.
The side of the square = diameter of the semicircle = 2/π.
The radius of semicircle = diameter/2 = [tex]\frac{2/\pi}{2} =\frac{1}{\pi}[/tex]
The perimeter of a semicircle = perimeter of a circle ÷ 2
[tex]Perimeter\ of \ semicircle = \frac{perimeter\ of\ circle}{2}=\frac{2\pi r}{2}=\frac{2\pi (\frac{1}{\pi} )}{2} =1\\ Perimeter\ of\ region = 4*Perimeter\ of \ semicircle=4*1=4\[/tex]
