Extreme Quadrilateral Areas

Geometry Level 3

We know by Heron's formula that if we know all the side lengths of a triangle, then we can determine the area of the triangle. However, this is not the case for a quadrilateral.

Find the maximum possible area of a quadrilateral with side lengths 3, 4, 5, and 6.

If this area can be expressed as \(P \sqrt Q\) for integers \(P \) and \(Q\), with \(Q\) square-free, find \(P+Q.\)

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