Browse · MATH
Printjmc
prealgebra senior
Problem
Each point in the hexagonal lattice shown is one unit from its nearest neighbor. How many equilateral triangles have all three vertices in the lattice? 
Solution
Number the points clockwise, beginning with the upper left as 1. Number the center point 7.
We can create six equilateral triangles with side length one: 176, 172, 273, 657, 574, and 473.
We can also create two equilateral triangles with side length : 135 and 246.
Thus, there are such equilateral triangles.
We can create six equilateral triangles with side length one: 176, 172, 273, 657, 574, and 473.
We can also create two equilateral triangles with side length : 135 and 246.
Thus, there are such equilateral triangles.
Final answer
8