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- Does the limit as n approaches infinity of the area of an n-sided polygon equal to the area of a circle?

Hello everyone!

I have been looking for a general equation for any regular polygon and I have arrived at this equation:

$$\frac{nx^{2}}{4}tan(90-\frac{180}{n})$$

Where

So I thought to myself "if the number of sides is increased as to almost look like a circle, does it result in the area of a circle?"

Is this:

$$\lim_{n\to\infty} \frac{nx^{2}}{4}tan(90-\frac{180}{n}) = \frac{C^{2}}{4\pi}$$

true?

I have been looking for a general equation for any regular polygon and I have arrived at this equation:

$$\frac{nx^{2}}{4}tan(90-\frac{180}{n})$$

Where

**x**is the side length and**n**the number of sides.So I thought to myself "if the number of sides is increased as to almost look like a circle, does it result in the area of a circle?"

Is this:

$$\lim_{n\to\infty} \frac{nx^{2}}{4}tan(90-\frac{180}{n}) = \frac{C^{2}}{4\pi}$$

true?

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