Respuesta :

the shaded area = 2 * area of the segment in each circle

area of 1 segment = area of sector - area of triangle formed by the 2 radii
                              = 1/2 * 4^2 * pi/3 -    2*2 sqrt3
                              = 8 pi/3  - 4 sqrt3
so area of shaded part =  2 * the above 
                                     = 16pi/3 - 8 sqrt3

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