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.

Answer 1

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).