The Dog's Span III

Calculus Level pending

A dog is tied on a point attaching a circular pillar with radius \(\large {\frac {43}{\pi^{2}}} \) m to a nearby straight fence as shown in the figure. If the length of the dog's chain is exactly enough to enclose the pillar, 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. Also assume that the dog cannot pass through the point attaching the pillar to the fence.

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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