Two identical circles intersect so that their centres and the points at which they intersect form a square of side 2 cm. What is the area (in cm²) of the portion that is common to the two circles ?

Radius of circle = AB = 2 cm.

Area of sector ABD = Area of sector BCD

$=\frac{1}{4} \pi r^{2}=\frac{\pi \times 4}{4}=\pi$ sq. $\mathrm{cm}$

Area of square $=4$ sq. $\mathrm{cm}$.

$\therefore$ Area of shaded region $=(2 \pi-4)$ sq. $\mathrm{cm}$.