(Canadian Senior Mathematics Contest 2024, Part A, Question 5, CEMC - UWaterloo)

In the diagram, $ABCDEF$ is a hexagon with six equal interior angles (that is, $\angle ABC = \angle BCD = \angle CDE = \angle DEF = \angle EFA = \angle FAB$).

Also, $BC = EF = 6$ and $AB = CD = DE = FA = 2$. Line segments $AC$, $BD$, $CE$, $DF$, $EA$, $FB$ create a smaller hexagon $PQRSTU$, as shown. If the area of hexagon $PQRSTU$ is $\frac{\sqrt{n}}{t}$, where $n$ and $t$ are positive integers with $t$ as small as possible, what is the ordered pair $(n, t)$?