Question 8
Hexagon $ABCDEF$ is divided into five rhombuses, $\mathcal{P},$ $\mathcal{Q},$ $\mathcal{R},$ $\mathcal{S},$ and $\mathcal{T},$ as shown. Rhombuses $\mathcal{P},$ $\mathcal{Q},$ $\mathcal{R},$ and $\mathcal{S}$ are congruent, and each has area $\sqrt{2006}.$ Let $K$ be the area of rhombus $\mathcal{T}.$ Given that $K$ is a positive integer, find the number of possible values for $K.$
