It could be a plane.
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The set of Pythagorean triple is three dimensional and infinitely large.
The answer depends on what your criterion for deciding what is "largest". Any rectangle will have an area of 47916 square feet. Its perimeter can be infinitely large.
There are two two-dimensional figure with an infinite length. They are rays, and lines.
A ray has one endpoint and continues in the other direction infinitely.
No because in Geometry, a plane goes on infinitely. No because in Geometry, a plane goes on infinitely.