Example 4 As shown in Figure 15-1, in the regular triangular frustum $A B C-A_{1} B_{1} C_{1}$, $S_{\triangle A B C}=\sqrt{3}, S_{\triangle A_{1} B_{1} c_{1}}=4 \sqrt{3}, D$ and $E$ are moving points on sides $A B$ and $A C$ respectively, and $D E / / B C$. The sum of the projection areas of the section $A_{1} D E$ and the section $B_{1} C_{1} E D$ on the base $A_{1} B_{1} C_{1}$ is ( ).
A. $\frac{\sqrt{3}}{3}$
B. $\frac{2 \sqrt{3}}{3}$
C. $\frac{4 \sqrt{3}}{3}$
D. $\frac{8 \sqrt{3}}{3}$
Solution: Choose D. Reason: When $D E \rightarrow A$, draw $A E \perp$ plane $A_{1} B_{1} C_{1}$, then the sum of the required projection areas is $S_{\triangle E B_{1} C_{1}}=$ $\frac{1}{2} \cdot B_{1} C_{1} \cdot E D_{1}>\frac{1}{2} \cdot B_{1} C_{1} \cdot A D=\frac{1}{2} \cdot 4 \cdot \sqrt{3}=2 \sqrt{3}$.
Also, the values of $\mathrm{A}$, $\mathrm{B}$, and $\mathrm{C}$ are all less than $2 \sqrt{3}$, so choose D. If we let $D E \rightarrow B C$ for estimation, it would be more complicated.