G4.2 In Figure $4, A B C D$ is a rectangle with $A B=\sqrt{\frac{8+\sqrt{64-\pi^{2}}}{\pi}}$ and $B C=\sqrt{\frac{8-\sqrt{64-\pi^{2}}}{\pi}} \cdot B E$ and $B F$ are the arcs of circles with centres at $C$ and $A$ respectively. If $b$ is the total area of the shaded parts, find the value of $b$.
$\begin{array}{l}=\frac{\pi}{4}\left(\frac{8+\sqrt{64-\pi^{2}}}{\pi}+\frac{8-\sqrt{64-\pi^{2}}}{\pi}\right)-\sqrt{\frac{64-\left(64-\pi^{2}\right)}{\pi^{2}}} \\ =\frac{\pi}{4}\left(\frac{16}{\pi}\right)-\sqrt{\frac{\pi^{2}}{\pi^{2}}}=4-1=3=b \\\end{array}$