Indian Institute of Foreign Trade 2009 Solved Paper

We can see that we will get a regular octagon as shown in the figure below.Let 'a' be the length of the side of the regular octagon
Hence, we can say that $\frac{\mathit{a}}{\sqrt{2}}+\mathit{a}+\frac{\mathit{a}}{\sqrt{2}}=2$
$\Rightarrow \mathit{a}=\frac{2}{\sqrt{2}+1}$
Area of a regular octagon $=2\times \left(1+\sqrt{2}\right)\times {\mathit{a}}^2$
$\Rightarrow 2\times \left(1+\sqrt{2}\right)\times {\left(\frac{2}{\sqrt{2}+1}\right)}^2$
$\Rightarrow \frac{8}{\left(\sqrt{2}+1\right)}$
Therefore, option D is the correct answer