A dog is tied on a triangular pillar with each side measuring 5 meters in the middle on an unfenced lot with infinite area. If the chain is 12 m long, what is the total span of area (in square meters) that the dog can reach? Assume the dog's size to be infinitesimal, and that the chain is not elastic.

Express your answer as floor \(\left \lfloor \large A \right \rfloor \) where A is the total span of area (in square meters) that the dog can reach.

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