# Pentagonal Problem

Geometry Level 3

Let $$ABCDE$$ be a convex pentagon. If $$P$$, $$Q$$, $$R$$ and $$S$$ are the respective centroids of the triangles $$ABE$$, $$BCE$$, $$CDE$$ and $$DAE$$, then which of the following is true :

$$A$$ : $$PQRS$$ is a parallelogram and its area is $$2/9$$ of that of $$ABCD$$.

$$B$$ : $$PQRS$$ is a rectangle and its area is $$2/9$$ of that of $$ABCD$$.

$$C$$ : $$PQRS$$ is a parallelogram and its area is $$1/3$$ of that of $$ABCD$$.

$$D$$ : $$PQRS$$ is a rectangle and its area is $$1/3$$ of that of $$ABCD$$.

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