(10 points) Xiao Hu uses 6 equilateral triangles, each with a side length of 1, to form shapes on a table without overlapping. Each triangle must share at least one side completely with another triangle, as shown in the figures below. What is the minimum perimeter of all the shapes that can be formed?
Problem 529
Official solution
【Analysis】First, analyze the minimum case, which is the situation with the most repeated edges.
【Solution】According to the problem:
The more edges overlap, the smaller the area.
Therefore, the minimum perimeter is: 6
The answer is: 6