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