Question

In th figure, ABCD, ABFE and CDEF are parallelograms. Prove that $ar\left(△ADE\right)=ar\left(△BCF\right)$

Answer 1

Given : In the figure, ABCD, ABEF and CDEF are || gms
To prove : ar $\left(△ADE\right)=ar\left(△BCF\right)$
Proof : $ABCDisa||gm$
$\therefore AD=BC$
Similarly, in || gm ABEF
AE = BF
and || gm CDEF,
DE = CF
Now, in $△ADEand△BCF$
AD = BC
DE = CF
AE = BF
$\therefore △ADE=△BCF\therefore ar\left(△ADE\right)=ar\left(△BCF\right)$