Question

Why area is considered both scalar and vector quantity

Answer 1

It has an area which is a scalar quantity and there is no way to assign a direction to that scalar quantity. At each point on that surface you can assign a vector normal to the surface, but that can’t be done consistently since a Möbius band is not orientable.

Answer 2

 Surface's area and whose direction is parallel to the unit normal vector. This vector then encodes both the magnitude and the direction of the surface.