Surface area is
a) Scalar
b) Vector
c) Neither scalar nor vector
d) Both scalar and vector
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A quantity which is neither a vector nor a scalar could be a tensor of rank two or of higher rank. As already mentioned moment of inertia is a tensor of rank two. Similarly conductivity of a substance could be a tensor of rank two. There can be many more examples of quantities which are tensor. To simplify our mathematics we make assumptions like that the substance is homogeneous ( ie its properties do not change with translation along an axis) and isotropic ( ie the properties of the substances do not change with rotation). It is under these simplifying assumptions that a symmetric tensor of rank two reduces to a scalar.
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