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# In Fig. 9.31, ABCD, DCFE and ABFE are parallelograms. Show that ar (ADE) = ar (BCF).

Q : 3    In Fig. $\small 9.31$,  ABCD, DCFE  and  ABFE are parallelograms. Show that  $\small ar(ADE)=ar(BCF)$.

Views

Given,

ABCD is a parallelogram. Therefore, AB = CD & AD = BC & AB || CD .......(i)

Now, $\Delta$ADE and $\Delta$ BCF are on the same base AD = BC and between same parallels AB and EF.
Therefore, ar ($\Delta$ADE) = ar($\Delta$BCF)

Hence proved.

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