geometry

What is the numerical value of the product of the lengths of all diagonals of a regular pentagon of side length 1?

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$\alpha=\frac{180°-72°}{2}=54°\\ sin\ \alpha =\frac{d}{2\cdot 1}\\ d=2\ sin\ \alpha=2\ sin\ 54°$

$d=1,618$

The numerical value of the product of the lengths of all diagonals is $1.618^5=11.09$

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