Hanoi Open Mathematics Competition 2013 Junior Question 6

Let \(ABC\) be a triangle of area \(1\text{ cm}^2\). Points \(D,E,F\) lie on \(AB,BC,CA\), respectively. Prove that \(\min\{[ADF],[BED],[CEF]\}\le\tfrac14\text{ cm}^2\), where brackets denote area.