Q5 of 24 Page 21

In the quadrilateral ABCD shown below, the sides AB and CD are parallel. M is the midpoint of the side BC.


The lines DM and AB extended, meet at N.


What is the relation between the areas of the quadrilateral ABCD and the triangle AND?

area of a parallelogram =

area of a triangle =


area of parallelogram = area(ABCD)


= area(ADMB) + area(Δ DCM) …(eq)1


Area of triangle = area(Δ AND)


= area(ADMB) + area(Δ BMN)


= area(ADMB) + area(Δ DCM) (from eq1) …(eq)2


∴ area of parallelogram = area of triangle


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AB = QR BC = RP CA = PQ


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In the quadrilateral ABCD shown below, the sides AB and CD are parallel. M is the midpoint of the side BC.


The lines DM and AB extended, meet at N.


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