It can be seen from the figure (of course, it needs to be proved a little when solving the problem, so I won't go into details here) that the hexagonal star is composed of 12 congruent small triangles, and the side length of the small triangle is 1/3 of the large equilateral triangle, so the area of the small equilateral triangle is 1/9 of the large equilateral triangle, so the small triangle.