I4.2 In Figure $1, \triangle B A C$ is a right-angled triangle, $A B=A C=m \mathrm{~cm}$. Suppose that the circle with diameter $A B$ intersects the line $B C$ at $D$, and the total area of the shaded region is $n \mathrm{~cm}^{2}$. Find the value of $n$.
$A B=A C=3 \mathrm{~cm} ; \angle A D B=90^{\circ}(\angle$ in semi-circle $)$
Shaded area $=$ area of $\triangle A C D=\frac{1}{2}$ area of $\triangle A B C=\frac{1}{2} \cdot \frac{1}{2} \cdot 3 \cdot 3 \mathrm{~cm}^{2}$
$$
n=\frac{9}{4}
$$