Black aerea in the normalised case

0) Area of the base square ${\displaystyle A_{0}=1}$
1) Area of the inscribed quarter circle ${\displaystyle A_{1}={\frac {\pi }{2}}\cdot r_{0}^{2}={\frac {\pi }{2}}\cdot ({\frac {1}{\sqrt {\pi }}})^{2}={\frac {\pi }{2}}\cdot {\frac {1}{\pi }}=0.5}$

B) ${\displaystyle B=A_{0}-A_{1}=0.5}$