Problem 4. Using vectors.

$$
\begin{aligned}
& \overline{H K}=\overline{A K}-\overline{A H}=\frac{1}{2}(\overline{A Q}+\overline{A N})-\frac{1}{2}(\overline{A M}+\overline{A P})= \\
& =\frac{1}{2}\left(\frac{1}{2}(\overline{A E}+\overline{A D})+\frac{1}{2}(\overline{A B}+\overline{A C})\right)- \\
& -\frac{1}{2}\left(\frac{1}{2} \overline{A B}+\frac{1}{2}(\overline{A C}+\overline{A D})\right)=\frac{1}{4} \overline{A E}
\end{aligned}
$$

Therefore, $A E=4 H K=4.8$.
Answer: 4.8.

![](https://cdn.mathpix.com/cropped/2024_05_06_d39e2e41eca8a5a4f1bcg-1.jpg?height=534&width=668&top_left_y=1726&top_left_x=1208)