11. 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, and 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 the decagon by a plane passing through points $C, W$ and $Q$ is $\frac{5488}{1755}$, $|A B|=5 / 9$, $|P Q|=10 \sqrt{2} / 9$. Find the distance between the bases of the decagon. Write the found value in the answer, rounding it if necessary.
Answer: 1.73 . (Exact value $\sqrt{3}(m=5 / 9, k=2)$.)