Construct any regular polygon (A003401) that has the same area as the sum of $n$ given triangles

Question

Original question: Construct any regular geometric shape that has the same area as given triangle?

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A003401

...and by construct I mean, suggest steps for construction or provide general idea

My idea is application of generalized Pythagora's theorem. Euclid Elements Book VI. $31$,

I know it's possible (and how) to construct such square and equilateral triangle

Euclid Elements Book VI. $18$, $\Rightarrow$ Every (regular) polygon can be visualized as multiple triangles

Answer 1

You can construct any regular polygon with 3 or more sides if you know the area, A, of the triangle you are trying to construct a similar scaled geometric shape from. Using $A$, create a regular polygon with n sides of side length:

$s = \sqrt{\frac{4A\tan(\frac{180}{n})}{n}}$

and with interior angle being:

$a = 180 - \frac{360}{n}$