# Every pentagon

**Geometry**Level pending

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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