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Question
In the given figure, M and N are the mid-points of the sides DC and AB respectively of the parallelogram ABCD.
If the area of parallelogram ABCD is 48 cm2;
(i) State the area of the triangle BEC.
(ii) Name the parallelogram which is equal in area to the triangle BEC.
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Solution
(i) Since triangle BEC and parallelogram ABCD are on the same base BC and between the same parallels i.e. BC // AD.
So Area ( ΔBEC )= `1/2 xx "Area" ( square`ABCD )
= `1/2` x 48 = 24 cm2
(ii) Area (` square "ANMD" ) = "Area" ( square` BNMC )
= `1/2"Area" ( square` ABCD)
= `1/2` x 2 x Area ( ΔBEC )
= Area ( ΔBEC )
Therefore, Parallelograms ANMD and NBCM have areas equal to triangle BEC.
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