In right triangle $PQR$, $\angle P = 90^\circ$, $PQ = 8$ units, and $PR = 6$ units. A line segment from point $P$ is drawn perpendicular to the hypotenuse $QR$ and intersects $QR$ at point $S$. Find the area of the quadrilateral $PQSR$. Let's think step by step and output the final answer within \boxed{}.
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