Question regarding electromagnetic induction?

Faraday's Law of Electromagnetic Induction states that the induced emf is directly proportional to rate of change of magnetic flux linkage. Magnetic flux linkage is given by N x B x A. So when there is a change in magnetic flux density B, to find magnetic flux linkage you will use N x A x (B2-B1). Thus, by saying that the change of area is 0 and thus emf will be 0, you are stating the Eletromagnetic Induction law as induced emf is directly proportional to the product of the rate of change of B, rate of change of A and the rate of change of N, which is a mistake from the actual Faraday's Law.