If two circles of unit radius intersect orthogonally, the common area of the circles is

Radius=1, Angle between circles= 90

$\boxed{Area of a sector=\frac{1}{2}{r}^2\theta }$

Required area = sector ABD area + sector BCD area -  square ABCD area

$2\left(\frac{1}{2}{\left(1\right)}^2\times \frac{\mathrm{\pi }}{2}\right)-1=\frac{\mathrm{\pi }}{2}-1$