Try it! Just a little geometry

Geometry Level 3

\(ABCD\) is a square which has an area of \(1\). \(E\) and \(F\) are points on the square's sides as shown in the figure above. \(\Delta AEF\) has a perimeter of \(2\). Diagonal \(BD\) divides \(\Delta ECF\) into two pieces: a smaller triangle and a quadrilateral. Which has a larger area?

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