I'd like to bring your attention to this *easy* geometry problem that I call "**The Green Zone Problem**". Let's suppose there is an imaginary city in the Middle-earth. I call this imaginary city as Indigo City (feel free to give any cool name) and its shape is a triangle like the picture below:

**Hint**: If the shape of Indigo City is an equilateral triangle, unless I'm very much mistaken, then its area is \(\dfrac{5a^2}{108}\sqrt{3}\).

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\[\color{blue}{\Huge-\hbar\alpha\rho\rho\gamma\,\,\,\rho r\sigma \beta l\epsilon m\,\,\,s\sigma l\nu \iota\eta g-}\]

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TopNewestAh, a nice way of introducing that wonderful property of X.

(Where X is to be determined by the reader)

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For an equilateral triangle, I'm getting \(\displaystyle \frac{2\sqrt{3}}{27}a^2\), with \(a\) being the side of the triangle. The boundaries of the green zone are made up of parabolas right? Unless I did something wrong here, then I have a method to generalise this.

This is the solution I got for an equilateral triangle: https://www.desmos.com/calculator/ao5sksutzx

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