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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.
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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