4. From a vertex $\mathrm{A}$ of a regular octagon $\mathrm{ABCDEFGH}$ with side length $\mathrm{a}$, draw a perpendicular line $\mathrm{AS}$ to the plane of the octagon. If $\mathrm{AS}=\mathrm{a}$, find the distance from $\mathrm{S}$ to $\mathrm{EF}$, the length of $\mathrm{SE}$, and the angle between $\mathrm{SE}$ and $\mathrm{CH}$.
(Ans: $\mathrm{SF}=\sqrt{4+2 \sqrt{2}} \mathrm{a}$, $\angle \mathrm{SEF}=\operatorname{arctg} \sqrt{4+2 \sqrt{2}})$