Maximize the Area

Geometry Level 4

Let \(ABCD\) be a convex quadrilateral with perimeter \(\frac{5}{2}\) and \(AC=BD=1\). Determine the maximum possible area of \(ABCD\).

If your answer is in the form \(\frac{p}{q}\), where \(p\) and \(q\) are coprime positive integers, determine \(p+q\).

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