Question 6
The graphs of the equations $$
\begin{aligned}y&=k,\\y&=\sqrt3x+2k,\\y&=-\sqrt3x+2k,\end{aligned}
$$ are drawn in the coordinate plane for $k=-10,$ $-9,$ $-8,$ $\ldots,$ $9,$ $10.$ These $63$ lines cut part of the plane into equilateral triangles of side $\frac{2}{\sqrt3}.$ How many such triangles are formed?
\begin{aligned}y&=k,\\y&=\sqrt3x+2k,\\y&=-\sqrt3x+2k,\end{aligned}
$$ are drawn in the coordinate plane for $k=-10,$ $-9,$ $-8,$ $\ldots,$ $9,$ $10.$ These $63$ lines cut part of the plane into equilateral triangles of side $\frac{2}{\sqrt3}.$ How many such triangles are formed?