In the given Figure, ABCD, DCFE, and ABFE are parallelograms. Show that ar(ADE) = ar(BCF).

Since ABCD is a parallelogram, therefore sides AD and BC are equal. Since DCFE is also a parallelogram, therefore, sides DE and FC are equal. Since ABFE is also a parallelogram, therefore, sides AE and BF are equal. So, triangles ADE and BCF are congruent by SSS congruency rule. ∴ Corresponding angles are equal in both triangles. So, the areas will be equal. Therefore ar(ADE) = ar(BCF).