Area form of a zero level set?

Question

Given a zero level set $f(x,y,z)=0$, is it correct that the area form represented as $\frac{dx \wedge dy}{f_z} = \frac{dy \wedge dz}{f_x} = \frac{dz \wedge dx}{f_y}$ when any of them is defined ? Thank you for your help.