2006 AIME I Problem 8

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

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.