Question

In parallelogram ABCD, E and F are any two points on the side AB and BC respectively. Show that
ar( △ADF)=ar( △DCE)
(hint- draw EG| |AD, FH| |AB)

Answer 1

Triangle DCE and parallelogram ABCD are on the same base and between the same parallels

Therefore ar(DCE)=1/2 ar(ABCD)...(1)

Similarly

ar(ADF)=1/2 ar(ABCD)...(2)

From 1 and 2 we get

ar(ADF)=ar(DCE)