346. Four villages are located at the vertices of a square with a side length of 2 km. The villages are connected by roads in such a way that it is possible to travel from any village to any other. Can the total length of the roads be less than 5.5 km?
346. If the roads are built as shown in Fig. 61 (A, B, C, and D are villages, roads are solid lines), then their total length will be $2+2 \sqrt{3}<5.5$. It can be shown that the specified arrangement of roads realizes the minimum of their total length.