In our math class (in the context of introduction to vectors) we were told that the projection of the vector area $S$ onto the $x$-$y$ plane is equal to the dot product of the vector area $S$ and the unit vector in $z$. We don't prove it however and it doesn't seem obvious to me. Why is this geometrically true?
Why does multiplying the area by $\cos(\text{angle})$ give the correct projection? I also can't seem to find an answer online as most places I searched just assumed this formula to be true. Thanks in advance (and sorry if this is obvious)!