Q. 24.4( 32 Votes )

Find the area of a quadrilateral PQRS in which QPS = SQR = 90°, PQ = 12 cm, PS = 9 cm, QR = 8 cm and SR = 17 cm (Hint: PQRS has two parts)


Answer :

Area of quadrilateral PQRS = area(ΔSQR) + area(ΔPQS)…(i)


Let us find area(ΔPQS)


Base = PQ = 12 cm


Height = PS = 9 cm


area of triangle = × base × height


area(ΔPQS) = × PQ × PS


area(ΔPQS) = × 12 × 9


area(ΔPQS) = 6 × 9


area(ΔPQS) = 54 cm2


Using pythagoras theorem


SQ =


SQ =


SQ =


SQ =


SQ = 15 …(ii)


Now let us find area(ΔSQR)


Base = QR = 8 cm


Height = SQ = 15 cm …from (ii)


area of triangle = × base × height


area(ΔSQR) = × QR × SQ


area(ΔSQR) = × 8 × 15


area(ΔSQR) = 4 × 15


area(ΔSQR) = 60 cm2


Therefore from (i)


Area of quadrilateral PQRS = area(ΔSQR) + area(ΔPQS)


= 60 + 54


= 114 cm2


Hence area of quadrilateral PQRS = 114 cm2


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