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# Calculate the area of the designed region in figure common between the two quadrants of circle of radius 8 cm each.

Here, 8 cm is the radius of the quadrants ABMD and BNDC.

Sum of their areas

$$= \ 2 \ × \ \frac{1}{4} \pi r^2 \ = \ \frac{1}{2} \pi r^2$$

$$= \frac{1}{2} \ × \ \frac{22}{7} \ × \ 64 \ = \ \frac{704}{7}$$ cm2

Area of the square ABCD

$$= \ 8 \ × \ 8 \ = \ 64$$ cm2

Thus, Area of the shaded region = Sum of the area of quadrants - Area of the square ABCD

$$= \frac{704}{7} \ - \ 64 \ = \ \frac{704 \ - \ 448}{7}$$

$$= \ \frac{256}{7}$$ cm2