Contained Region

When we join the centers of the three circles, we get an equilateral triangle. The green region is formed by three arcs of $60 ^\circ$ sectors.

Since the radius of the unit circle is $1$ , its perimeter is $2\pi \times 1 = 2 \pi$ . The arc length of a $60^\circ$ sector of a unit circle is $\dfrac{60^\circ}{360^\circ}$ th the perimeter of a unit circle, which is $\dfrac{60^\circ}{360^\circ} \times 2\pi = \dfrac\pi3$ . Since three such sectors form the border of the green region, the perimeter of the green region is $3 \times \dfrac\pi3 = \pi$ .

perimeter of the green region=3*2 pi r/6=pi