I agree with your formula and numbers, but you are carrying too many significant figures, especially with the cosine. There should only be two significant figures.
I have preferred to avoid Electricity and Magnetism questions because I don't remember the subject very well, and my favorite college textbook on that subject was destroyed in a house fire.
A constant magnetic field passes through a single rectangular loop whose dimensions are 0.35 m x 0.55 m. The magnetic field has a magnitude of 2.1 T and is inclined at an angle of 55° with respect to the normal to the plane of the loop.
(a) If the magnetic field decreases to zero in a time of 0.37 s, what is the magnitude of the average emf induced in the loop?
_________V
Emf = -N cos theta (B-B0/t-t0)
Emf = -1(cos 55degrees)(0-2.1T/0.37s-0)
Emf = -1(0.573576436)(-2.1T/0.37s)
Emf = (-0.573576436)(-5.675675676)
Emf = 3.25543 V
(b) If the magnetic field remains constant at its initial value of 2.1 T, what is the magnitude of the rate (delta A) / (delta t) at which the area should change so that the average emf has the same magnitude as in part (a)?
_________m^2/s
delta A/ delta t= Emf / NB cos theta
= 3.25543 V / (1)(2.1T)(cos 55 degrees)
= 2.7027 m^2/s
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