In a quadrilateral PQRS ,diagonal PR and QS intersects at O such that ar（POS）=ar（QOR）. If distance between PQ and SR is 4 cm,PQ=3 cm and SR =7cm .Find ar（PQRS）
Answers
Answer:
20 Square cm
Step-by-step explanation:
See the attached details for the details.
PQRS is quadrilateral.
Area(POS) = Area(QOR)
Adding Area(SOR) to both sides.
Area(POS) + Area(SOR) = Area(QOR) + Area(SOR)
If you look at the diagram, LHS = Area(PSR), RHS = Area(QSR)
Hence Area(PSR) = Area(QSR).
ΔPSR and ΔQSR have same base and areas are same.
Hence heights of both triangles are same. (Area of triangle = base*height/2. Base of both are same, so heights should be same)
From above we can conclude that, PQ and SR are parallel to each other.
That means, PQRS is a trapezoid.
Given that PQ = 3 cm SR = 7 cm. Distance between PQ and SR = 4 cm.
Area(PQRS) = Area of Trapezoid = (PQ + SR)*(Distance between PQ and SR)/2
= (3+7) * 4/2 = 20 Square cm.
Step-by-step explanation:
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