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.

Answer 1

(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.