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# geometry

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

Sep 5, 2021

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

Hello Guest!

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

$$d=1,618$$

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

!

Sep 5, 2021