1. The decagon $A B C D P Q R S T U V W$ has two parallel bases: square $A B C D$ and octagon $P Q R S T U V W$, all angles of which are equal, as well as eight lateral faces: triangles $A P Q, B R S, C T U, D V W$ and rectangles $D A P W, A B R Q, B C T S$ and $C D V U$. It is known that the area of the section of this decagon by a plane passing through points $A$, $S$ and $U$ is $\frac{143}{20},|A B|=1,|P Q|=\sqrt{2}$. Find the distance between its bases. Write the found value in the answer, rounding it if necessary.
Answer: 3.61 . (Exact value $\sqrt{13}(m=1, k=1)$.)