smc

Here is an easy way to look at this, where $p$ is the perimeter, and $a$ is the apothem: Area of Octagon: $\frac{ap}{2}=1$. Area of Rectangle: $\frac{p}{8}\times 2a=\frac{2ap}{8}=\frac{ap}{4}$. You can see from this that the octagon's area is twice as large as the rectangle's area is $\boxed{\frac{1}{2}}$.