Area of common region between intersecting circles

Let the two centers be $O_1$ and $O_2$ and intersection points be $P$ and $Q$. $O_1 P O_2 Q$ forms a square of side 1 cm. Thus, radius of each circle $r = 1$ cm. The common area consists of two identical circular segments. Area of sector with central angle $90^\circ = \frac{1}{4} \pi r^2 = \frac{\pi}{4}$. Area of triangle formed by center and intersection points $= \frac{1}{2} \times 1 \times 1 = \frac{1}{2}$. Common area $= 2 \times \left(\frac{\pi}{4} - \frac{1}{2}\right) = \frac{\pi}{2} - 1$.