Area is a vector quantity...why???

Yes, It is a Vector quantity,If you are dealing with physics problems where a volume is enclosed by a  closed surface. Especially when we are having a vector field like electric field  and magnetic field enclosed in a closed surface. we define a quantity called flux which is related to number of lines of force of the field passing through the surface area. we have to consider area as a vector quantity as we change the angle or orientation of the surface area the number of lines of force change significantly. It is possible that the lines of force crossing the area become zero in some orientation. so to include the effect of angle and orientation from a perticular reference we need to consider area as vector quantity. We can look it up in Gauss divergence theorem.

Commoly area is a scalar quantity because there is no need of direction to define and also follow the algebrac summation. When we talk about vector there exist a frame of reference with a certain origin. Dealing with physical quantity,  which depends upon area, we have to treat area as vector field which is known as areal vector. Still only area is a scalar.

Yes, scalar and Yes, vector depending on the situation.

CASE-1

Let us take example for SCALAR:

A human being wants to find out area of his farm. Then, area is scalar.

But, why NOT VECTOR?

It is because of the logic that we define things depending on the context. Here, why would you require direction of an area. So, here we define area as a SCALAR quantity.

CASE II: VECTOR

In electromagnetism, we often require the direction of a loop, say if a conducting wire on a surface has current flowing through it in CLOCKWISE direction then it has area VECTOR pointing inwards i. e. into the plane of paper. Whereas, when we flip the wire so that the current flows in ANTI CLOCKWISE direction, then the area VECTOR points outwards i. e. outside plane of the paper. In this case, area is a vector.