When does $|K| = \frac{|N_u \times N_v|}{|\phi_u \times \phi_v|}$ where $\phi(u,v)$ gives a surface, and prove this.

Question

So, my tutor has said that we can always parameterise a surface such that this equation is true. So there seems to either always be a parameterisation like this, or this is always true. I'm not sure, and I can't prove it.

I've seen that $|\phi_u \times \phi_v| = \sqrt{\det g}$ on another question here, so I guess then somehow $|N_u \times N_v| = \frac{\det h}{\sqrt{\det g}}$? I'm not sure, or if I'm even on the right track.

Can I have any help or advice? Thank you!