I know why cross product is used and how to use it. I also understand that, for doing math we need to consider a direction for the result we have got by doing cross product vector multiplication.
But actually why is this direction considered perpendicular to the area? Is there any specific reason or is this just a traditional way?
This is as the case because the standard/euclidean scalar product $<-,->$ of the cross-product $v \times u$ with the vectors v and u is zero and therefor, by linearity, zero for all vectors in the plane that is generated by v and u. And perpendicularity, or rather orthogonality, in respect to a scalar product, is defined by the scalar product being zero.
If you are now wondering why the cross-product points in one of two direction, this depends on the order of your cross product as $u \times v = - v \times u$, this is the convention, maybe because this is compatible with the mathematical direction, counter clockwise, if you go through $u,v,u \times v$.