Grazing Cow

Geometry Level 3

A cow is tied to a corner (vertex) of a regular hexagonal fenced area of sides \(4\) meters long, with a rope of length \(10\) meters long, in a grass field. The cow cannot graze inside the fenced area. What is the maximum possible area of grass field in which the cow can graze?

Let \(A\) be the area in square meters. Find \(\left\lfloor A \right\rfloor \). where \( \left\lfloor ... \right\rfloor \) represents Greatest Integer Function.

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