[tex]\it MN=\dfrac{AD+BC}{2} \Rightarrow 2MN=AD+BC \Rightarrow AD+BC=2MN\ \ \ \ \ (*)\\ \\ \\ \begin{cases} \it MN+AD=31\\ \\ \it MN+BC=25\end{cases}\ \Rightarrow 2MN+AD+BC=56 \stackrel{(*)}{\Longrightarrow}\ 2MN+2MN=56|_{:2} \Rightarrow\\ \\ \\ \Rightarrow MN+MN=28 \Rightarrow MN=14\ cm[/tex]
