1.82 Draw the following lines on the coordinate plane:
$$
y=k, y=\sqrt{3} x+2 k, y=-\sqrt{3} x+2 k,
$$

where $k=0, \pm 1, \pm 2, \cdots, \pm 10$. These 63 lines can divide the plane into several equilateral triangles. Find the number of equilateral triangles with side length $\frac{2}{\sqrt{3}}$.
[Solution] The outer 6 straight lines form a regular hexagon with a side length of $\frac{20}{\sqrt{3}}$. The 3 straight lines passing through the origin
$$
y=0, y=\sqrt{3} x, y=-\sqrt{3} x
$$

divide this regular hexagon into 6 equilateral triangles, each with a side length of $\frac{20}{\sqrt{3}}$. Since the side length of each such large triangle is 10 times that of the small triangles in question, each large triangle can be divided into 100 small triangles. Therefore, the regular hexagon is divided into 600 equilateral triangles with a side length of $\frac{2}{\sqrt{3}}$. Additionally, there are 60 small equilateral triangles located outside the regular hexagon, with one side lying on the side of the hexagon, 10 on each side of the hexagon. Thus, the total number of equilateral triangles with a side length of $\frac{2}{\sqrt{3}}$ is 660.