[ [Ratio of areas of triangles with a common base or common height] Rearrangement of areas Pentagons

Given a convex pentagon $A B C D E$. The area of each of the triangles $A B C, B C D, C D E, D E A, E A B$ is $S$. Find the area of the given pentagon.

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Prove that the diagonals of the given pentagon are parallel to its sides.

## Answer

$\frac{(5+\sqrt{5}) S}{2}$