Question

PQRS is a quadrilateral in which diagonal QS measures 48 cm. PM and RN are perpendiculars to QS, such that PM and RN measure 14.7 cm and 17.3 cm respectively. The area of quadrilateral PQRS is

Answer 1

Here ,

diagonal ( d ) = QS = 48 cm

h1 = PM = 14.7 cm

h2 = NR = 17.3 cm

area of PQRS = [ ( h1 + h2 )d ]/2

A = [ ( 14.7 + 17.3 ) 48 ]/2

A = ( 32 × 48 )/2

A = 32 × 24

A = 768 square cm

I hope this helps you.

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Answer 2

PQRS is a quadrilateral in which diagonal QS = 48cm . PM and RN are perpendiculars to QS , such that PM and RN measure 14.7 cm and 17.3 cm respectively .

see figure,
area of quadrilateral PQRS = area of ∆PQS + ∆RQS

= 1/2 × base , QS × altitude, PM + 1/2 × base, QS × altitude , RN

= 1/2 × 48 × 14.7 + 1/2 × 48 × 17.3

= 1/2 × 48( 14.7 + 17.3)

= 24 × 32

= 768 cm²

hence, area of quadrilateral PQRS = 768 cm²