Track / Stage 4 / 241 of 340 #501 of 1964

Problem 501

AMC 12 late, AIME early

Geometry Difficulty 4.9 Find the answer

10. (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? $\qquad$

Your answer

A number or a short expression. Spacing and $ signs are ignored.

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

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.