Question 4
Patio blocks that are regular hexagons $1$ unit on a side are used to outline a garden by placing the blocks edge to edge with $n$ on each side. The diagram indicates the path of blocks around the garden when $n = 5.$
If $n = 202,$ then the area of the garden enclosed by the path, not including the path itself, is $m\left(\frac{\sqrt{3}}{2}\right)$ square units, where $m$ is a positive integer. Find the remainder when $m$ is divided by $1000.$
If $n = 202,$ then the area of the garden enclosed by the path, not including the path itself, is $m\left(\frac{\sqrt{3}}{2}\right)$ square units, where $m$ is a positive integer. Find the remainder when $m$ is divided by $1000.$