Why does induced current direction depend on area vector orientation?

[Gabriele Pinna]

If there is a rotating wire in a constant magnetic field what is the direction of the induced current ?
The problem is the direction of the area vector which is arbitrary, if it is parallel to the magnetic field the current will flow in a direction, if it is anti-parallel it will flow in the opposite direction.
What is wrong ?

 

[Dale]

Are you familiar with Lenz's law?