Question

in the fig PTllQR and QT ll RS .show that ar(triangle PQR)=ar(triangle QTS)

Answer 1

Construction => Join TR 
triangle (QTS) and triangle (QTR) lie on same base QT and b/w sane parallels QT and RS 
therefore,their areas are equal 
ar(QTS) = ar (QTR).....[1] 

triangle (PQR) and triangle (TQR) lie on the same base QR and b/w same parallels PT and QR 
therefore,their areas are equal 
ar(PQR) = ar (QTR)....[2] 
BY [1] & [2] 
ar(QTS) = ar(PQR)