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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