Andrea inscribed a circle inside a regular pentagon and circumscribed a circle around it, calculating the area of the region between the two circles. Bethany performed the same operations with a regular heptagon (7 sides). The areas of the two regions were $A$ and $B$, respectively. Each polygon had a side length of $2$. The relationship between $A$ and $B$ can be expressed in the form $A = kB$. Please find the value of $k$.

Let's think step by step and output the final answer within \boxed{}.
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