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What does n stand for in the expression?If there are 60 sides, what is the difference between the perimeter and π?

What does n stand for in the expression?If there are 60 sides, what is the difference-example-1

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a. The expression represents the perimeter of a polygon:


n\cdot\sin ((360)/(2n))

n represents the number of sides of the polygon.

b. If we have 60 sides, then n = 60.

We can calculate the approximation given by the expression as:


\begin{gathered} n\cdot\sin ((360)/(2n)) \\ 60\cdot\sin ((360)/(2\cdot60)) \\ 60\cdot\sin ((360)/(120)) \\ 60\cdot\sin (3) \\ 60\cdot0.0523 \\ 3.138 \end{gathered}

We can then calculate the difference with π using a calculator as:


|3.138-\pi|=0.0036

The difference is approximately 0.0036.

User Suryansh Singh
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