Why Do We Need Vector Area?

Vector area is quite an essential quantity used in various equations in physics. We know that vector area is a vector quantity with the magnitude of area of a surface and a position vector perpendicular to the plane of that surface. But have you ever thought, why is the position vector normal to the plane? Most of us never give this question a thought, but it is very important to have an intuitive understanding of this. For this, I will give a very simple example. Consider a flat circular surface. When we look at the surface from directly above, we see a circle. But if we see it from a certain angle, its shape will change in a 2-dimensional plane, and in this case, it will become ellipse. You see, just by changing the angle from which we see a surface, the information about its shape changes. The angle that describes the shape of a surface correctly is 90 degrees. If we want to calculate the area of a surface and we don't see the surface from directly above,i.e., 90 degrees, we will interpret wrong information about the shape of the surface and hence, we will not get the correct value of the area. That is why when we are using area as a vector, we need the position vector to be describing the shape of the surface correctly, so we can calculate the area correctly. And for that, the only angle is the angle perpendicular to the surface,i.e., 90 degrees.