The answer is 67.725.

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So, my thinking is right!!!! :)

Vinayak Srivastava
- 10 months, 3 weeks ago

I don't know if what I did was right, but I assumed a $2020-$ gon as a circle!

$\pi r^2 =365 \implies r \approx 10.778$ $\implies 2\pi r \approx \boxed{67.72}$

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The formula to get the area of a regular polygon is:

$\large A = \frac{1}{4}ns^{2} \cot\left(\frac{π}{n}\right)$ $\small \begin{array}{lcl} n & = & \text{the number of sides of the polygon.} \\ s & = & \text{side length of the polygon.} \end{array}$

$\small \begin{array}{cccl} & 365 & = & \dfrac{1}{4}(2020)(s^{2}) \cot\left(\dfrac{π}{2020}\right) \\[1em] \implies & s & = & \dfrac{2 \sqrt{365} \sqrt{\tan \left( \dfrac{π}{2020} \right) }}{ \sqrt{2020}} \\[1em] & s & \approx & 0.033527 \end{array}$

Multiplying the side length by $2020$ , we get the perimeter $\boxed{\approx 67.725}$ .

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Refine how?

Pi Han Goh
- 10 months, 3 weeks ago

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The array looks cramped. It doesn't look good.

Kaizen Cyrus
- 10 months, 3 weeks ago

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Original: $\begin{array} { c c c } a & = & \frac12 \\ & = & \frac36 \end{array}$

Modified 1: $\begin{array} { c c c } a & = & \frac12 \\[0.5em] & = & \frac36 \end{array}$

Modified 2: $\begin{array} { c c c } a & = & \frac12 \\ \phantom{0} \\ & = & \frac36 \end{array}$

Code:

Pi Han Goh
- 10 months, 3 weeks ago

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@Pi Han Goh – Thank you for this.

Kaizen Cyrus
- 10 months, 3 weeks ago

@Pi Han Goh – What does \phantom{0} do $\phantom{0}$

Mahdi Raza
- 10 months, 2 weeks ago

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@Mahdi Raza – Tell the LaTeX system to put an invisible object that can't be seen.

Pi Han Goh
- 10 months, 2 weeks ago

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Pi Han Goh
- 10 months, 2 weeks ago

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@Pi Han Goh – Alright. Any colour as well? $\red{\text{This is a trial} \phantom{0 \text{ test}}}$ \ ( \red{\text{This is a trial} \phantom{0 \text{ test}}} \ )

- $\red{\text{This is also a trial} \phantom{0} \text{ test}}$ \ ( (\red{\text{This is also a trial} \phantom{0} \text{ test}}\ )

Mahdi Raza
- 10 months, 2 weeks ago

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@Mahdi Raza – What you did is basically correct. You should see Pall Marton's note about coloring too, I got to learn something new from his note too.

Pi Han Goh
- 10 months, 2 weeks ago

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@Pi Han Goh – I'll check it out, looks interesting and well made

Mahdi Raza
- 10 months, 2 weeks ago

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Since there are so many sides, we can assume that the regular polygon is a circle. Then the perimeter is the circumference or

$2\pi r = 2 \pi \cdot \sqrt{\frac {365}\pi} = 2 \cdot \sqrt{365\pi} \approx 67.725$

The same answer up to three decimal places..

So need no formula when the sides are many