【Answer】4 square meters
【Solution】As shown in the figure, let $MG=x, EN=y$
Obviously, $\triangle MGF \sim \triangle FEN$, so: $\frac{x}{2}=\frac{1}{y} \Rightarrow xy=2$
$S_{\triangle MGF}=\frac{x}{2}, \quad S_{\triangle AE:}=y$
Find the minimum value of $\frac{x}{2}+y$
$\frac{x}{2}+\frac{2}{x} \leq 2 \times \frac{x}{2}+\frac{2}{x}=2$
$\therefore \frac{x}{2}+y$ minimum value is 2.
The minimum area is: $2+1 \times 2=4\left(\mathrm{~m}^{2}\right)$.
16. A rectangular thin wooden board, 7 meters long and 5 meters wide, has a small rectangular area at one corner damaged by insects, the damaged part is 2 meters long and 1 meter wide. Please design a method to saw off the damaged area in one straight cut, making the area removed as small as possible. What is the minimum area to be removed? Explain your reasoning.