G2.2 In Figure 2(a), $A B C D$ is a rectangle. $D E: E C=1: 5$, and $D E=12^{\frac{1}{4}} . \triangle B C E$ is folded along the side BE. If $b$ is the area of the shaded part as shown in Figure 2(b), find the value of $b$.

G2.3 Let the curve $y=x^{2}-7 x+12$ intersect the $x$-axis at points $A$ and $B$, and intersect the $y$-axis at $C$. If $c$ is the area of $\triangle A B C$, find the value of $c$.
Let $D E=t$, then $C E=5 t$. Suppose $B C^{\prime}$ intersects $A D$ at $F, C^{\prime} E$ intersects $A D$ at $G$.
$$
\begin{array}{l}
B C=B C^{\prime}=A D=5 t \tan 60^{\circ}=5 \sqrt{3} t \\
\angle C^{\prime} E D=60^{\circ}, \angle A B C^{\prime}=30^{\circ}, \angle C^{\prime} F G=60^{\circ}, \angle C^{\prime} G F=30^{\circ} \\
A F=6 t \tan 30^{\circ}=2 \sqrt{3} t, D G=t \tan 60^{\circ}=\sqrt{3} t \\
F G=5 \sqrt{3} t-2 \sqrt{3} t-\sqrt{3} t=2 \sqrt{3} t \\
C^{\prime} F=2 \sqrt{3} t \cos 60^{\circ}=\sqrt{3} t, C^{\prime} G=2 \sqrt{3} t \cos 30^{\circ}=3 t \\
\text { Area of } \triangle C^{\prime} F G=\frac{1}{2} \sqrt{3} t \times 3 t=\frac{3 \sqrt{3}}{2} t^{2}=\frac{3 \sqrt{3}}{2} \sqrt{12}=9 \\
x^{2}-7 x+12=(x-3)(x-4)
\end{array}
$$

The $x$-intercepts of 3,4 .
Let $x=0, y=12$
$$
c=\frac{1}{2}(4-3) \cdot 12=6 \text { sq. units }
$$