But if the original square had an initial surface of S2 =1 sq units, that is, side of 1 times side of 1 = 1 sq unit, how can the resulting shape, that is, distorting a square to form a hyperbolic paraboloid, have a surface area of 5.708 sq units??

Q: .what does the axis of symmetry do to the parabola?

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A: The given problem is solved below in detail.