IMAC 2010

$3n$ points are given ( $n\ge 1$ ) in the plane, each $3$ of them are not collinear. Prove that there are $n$ distinct triangles with the vertices those points.

Find all functions $f: \mathbb{R}\to\mathbb{R}$ such that we have $f(x + y) = f(x) + f(y) + f(xy)$ for all $x,y\in \mathbb{R}$