G4.2 In Figure 1 , let $A B, A C$ and $B C$ be the diameters of the corresponding three semi-circles. If $A C=B C=1 \mathrm{~cm}$ and the area of the shaded region is $R \mathrm{~cm}^{2}$. Find the value of $R$.
Reference: 1994 HI9
$$
A B=\sqrt{2}
$$

Shaded area $=R \mathrm{~cm}^{2}=S_{\text {circle with diameter } A C}-2 S_{\text {segment } A C}$
$$
R=\pi\left(\frac{1}{2}\right)^{2}-\left[\frac{1}{2} \pi \cdot\left(\frac{\sqrt{2}}{2}\right)^{2}-\frac{1}{2} \cdot 1^{2}\right]=\frac{1}{2}
$$