Let $G(n)$ denote the largest possible area of an $n$-gona polygon with $n$ sides contained in the region $\{(x, y) \in \Bbb R^2: x^4 \leq y \leq 1\}$.
For example, $G(3) = 1$ and $G(5)\approx 1.477309771$.
Find $G(101)$ rounded to nine digits after the decimal point.
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