The sides of the blue and green equilateral triangles are respectively parallel. The perimeter of the blue triangle is 4, and the perimeter of the green triangle is 5. Find the perimeter of the hexagon formed by the intersection of these triangles.

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The sum of the perimeters of the blue and green triangles is equal to the sum of the perimeters of the six small triangles surrounding the hexagon.

## Solution

Notice that the sum of the perimeters of the blue and green triangles is equal to the sum of the perimeters of the six small equilateral triangles surrounding the hexagon. Each side of the hexagon is $1 / 3$ of the perimeter of the corresponding triangle. Therefore, the perimeter of the hexagon is one third of the sum of the perimeters of the blue and green triangles, i.e., it is 3.

## Answer

## Problem