There are $n$ points inside a $1\times1$ square that can form a convex polygon. Can $3$ of them exist, such that $\mathcal{A}\le\frac{8}{n^2}$?

Question

There are $n$ points inside a $1\times1$ square that can form a convex polygon. Can $3$ points of them exist, such that $\mathcal{A}\le\frac{8}{n^2}$?

where $\mathcal{A}$ area of triangle formed by these three points.

How we can solve this problem using Pigeon-Hole Principle?