In the figure, ABCD is aparallelogram in which BCis produced to E such thatCE = BC. AE intersects CDat F. Show that ar (∆BDF)= 14ar (ABCD).

Try this. I just googled

ABCD is aparallelogram in which BCis produced to E such thatCE = BC

and got this hit, among others:

http://www.meritnation.com/ask-answer/question/abcd-is-a-parallelogram-in-which-bc-is-produced-to-e-such-th/areas-of-parallelograms-and-triangles/6686713

It is the same problem, just approached from a different side (as it were).