# Puzzle with the point inside paralelogram and area

We have a paralelogram $$ABCD$$ and point $$P$$ inside it. Halflines $$BP$$ and $$DP$$ cuts respectively lines $$AD$$ and $$AB$$ at $$E$$ and $$F$$. Why are the area of $$ABPD$$ and $$CEPF$$ the same regardles of the position of $$P$$?

This is again some contest problem (I think), I had it in my notes for a long time (at least 10 years) and I thought it would be interesting for this site. I solved it only recently.