Question 7
Let $PQRS$ be a trapezoid such that $PS\parallel QR$ and $T$ is the intersection point of $PR$ and $QS$, as shown in the diagram below. Let $I$, $M$ and $C$ be the midpoints of $ST$, $PQ$ and $RT$, respectively. If $\angle STR=120^\circ$, $\angle SQR=\angle SPR$ and the area of triangle $IMC$ is equal to $1024\sqrt3$ square centimeters, then find the length, in centimeters, of $PQ$.
