# 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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