Bài giải:

${{S}_{ABC}}=\frac{1}{2}AH.BC=5\left( c{{m}^{2}} \right)$

Vì $\Delta AMN\backsim \Delta ACB\left( g.g \right)$ nên $\frac{{{S}_{AMN}}}{{{S}_{ABC}}}={{\left( \frac{MN}{BC} \right)}^{2}}={{\left( \frac{AH}{BC} \right)}^{2}}=\frac{4}{25}$

$\Rightarrow {{S}_{AMN}}=\frac{4}{25}.5=\frac{4}{5}\left( c{{m}^{2}} \right)$

$\Rightarrow {{S}_{AMHN}}=\frac{8}{5}\left( c{{m}^{2}} \right)$

Đáp án đúng là C