VN-TST 1996 Problem 1

In the plane we are given $3 \cdot n$ points ( $n>$ 1) no three collinear, and the distance between any two of them is $\leq 1$ . Prove that we can construct $n$ pairwise disjoint triangles such that: The vertex set of these triangles are exactly the given 3n points and the sum of the area of these triangles $< 1/2$ .