- Join $R,X$ and $T,X$
- Look for triangles that have equal bases and altitudes and notice that $\triangle PXY= \triangle RXT$.
- Think about breaking $\triangle PXT$ into $\triangle PXR$ and $\triangle RXT$.
- Work with $\triangle PXT$ and $\triangle TQS$ and also $\triangle PXR$ and $\triangle RQS$ and then break $\triangle TQS$ into suitable triangles.
- Try to prove that, $\triangle LST$ = $\triangle PXY$+$\triangle LQR$