6 A regular tetrahedron $D-ABC$ has a base edge length of 4 and a side edge length of 8. A section $\triangle AEF$ is made through point $A$ intersecting side edges $DB$ and $DC$. What is the minimum perimeter of $\triangle AEF$? $\qquad$ .
6 11 Hint: Draw the lateral development of the triangular pyramid, and from the minimum perimeter of $\triangle A E F$, we get $A$, $E, F, A_{1}$ are collinear. It is easy to see that $E F / / B C$, thus the isosceles $\triangle D A B \sim \triangle A E B$, $A E=A B=4$,
$$
\frac{B E}{A B}=\frac{A B}{D A}=\frac{1}{2},
$$

which means $B E=2, D E=6$,
$$
\frac{E F}{B C}=\frac{D E}{D B}=\frac{6}{8}=\frac{3}{4},
$$

so $E F=3$, and by $A_{1} F=A E=4$, then
$$
A A_{1}=A E+E F+F A_{1}=11 .
$$