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Question
In the figure, PQR is a straight line. SQ is parallel to Tp. Prove that the quadrilateral PQST is equal in area to the ΔPSR.
Solution
In quadrilateral PQST,
ar(ΔPQS) = `(1)/(2)` x ar(quadrilateral PQST)
ar(quadrilateral PQST) = 2ar(ΔPQS) .......(i)
In ΔPSR,
ar(ΔPSR) = ar(ΔPQS) + ar(ΔQSR)
but ar(ΔPQS) = ar(ΔQSR) ...(since QS is median as QS || TP)
ar(ΔPSR) = 2ar(ΔPQS) ........(ii)
From (i) and (ii)
ar(quadrilateral PQST) = ar(ΔPSR).
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