G2.2 In Figure $1, \triangle A B C$ is a right-angled triangle, $A B=3 \mathrm{~cm}$, $A C=4 \mathrm{~cm}$ and $B C=5 \mathrm{~cm}$. If $B C D E$ is a square and the area of $\triangle A B E$ is $b \mathrm{~cm}^{2}$, find the value of $b$.
$$
\cos B=\frac{3}{5}
$$

Height of $\triangle A B E$ from $A=A B \cos B=3 \times \frac{3}{5}=\frac{9}{5}$
$$
b=\frac{1}{2} \cdot 5 \times \frac{9}{5}=\frac{9}{2}
$$