A small garden

Geometry Level 5

A gardener wants to create a closed fenced field. However, he only has 4 different fencing lengths: one of 1m, one of 2m, one of 3m and one of 4m. If the maximum area that can be fenced can be represented as \(a \sqrt{b}\), where \(a\) and \(b\) are positive integers and \(b\) is squarefree, find \(a+b\).

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