2. As shown in the figure, the length of rectangle $A B C D$ is $B D=8$ cm, and the width is $C D=6$ cm. $E$ is a point on line segment $B C$. When triangle $A B E$ is folded along line $A E$, point $B$ coincides with point $F$ on $A C$. Find the area of triangle $C E F$.
2.【Answer】Let $B E=E F=x(\mathrm{~cm}), A C^{2}=8^{2}+6^{2}, A C=10$
$$
\begin{array}{l} 
6 \cdot x \div 2 \times 2+(10-6) \cdot x \div 2=6 \times 8 \div 2 \\
6 x+2 x=24 \\
8 x=24 \\
x=3 \\
S_{\triangle C E F}=3 \times 4 \div 2=6 .
\end{array}
$$