Every pentagon

On the perimeter of a square, fix a starting point. Mark out every fifth of the perimeter, and connect up these 5 points to form a pentagon. For example, if we started out with the top left corner, we will obtain:

Let $x$ be the ratio of the area of the pentagon to the square. If the difference of the maximum and minimum values of $x$ can be expressed in the form $\large \frac {a}{b}$ , where $a$ and $b$ are coprime positive integers, determine the value of

$3 \times (a + b)$ .

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This is where the problem has been derived