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No.
It was named after a pentagon, it wasn't the 'Pentagon' that named the 'pentagon'.
Hexagon * * * * * A pentagon
Its from the greek word pente (πεντε) meaning five (5). Also the other part of pentagon is greek. It means ''angle''. Pentagon means (a structure) that has five angles.
Because it's shaped like a pentagon. A pentagon is a five-sized shape.