The magnetic flux in the loop is $\Psi =\int \vec{B}\cdot d\vec{A}= \vec{B}\cdot \vec{A(t)} =B d h \cos\omega t$
So the induced emf $\epsilon= -\frac {d\Psi}{dt}=B (dh) \omega \sin\omega t=BA_{max} \omega \sin\omega t$
is $\Psi =\int \vec{B}\cdot d\vec{A}= \vec{B}\cdot \vec{A(t)} =B d h \sin\omega t$