i need to know the coordinates of the verticies of a regular polygon that can fit in a square with side length 10. it needs to be as big as possible. i've tried and failed multiple times. i usualy get stuck trying to find the length of a side of the pentagon, but i do it once, get one answer, do it again, get a different answer, about 4 times over. note: this is NOT for school purposes.
If you really want the largest area regular polygon that fits within a 10 by 10 square, it will an "infinitygon" or a circle.
If you want the largest pentgon that fits within a 10 by 10 square:
1--You know the central angles of each of the 5 triangles forming the pentagon.
2--You can then get the side of the pentagon.
3--You can then get the apaothem of each triangle.
4--You can then get the area of the pentagon.
5--The width will be 10.00 but the height will be 9.5105.
6--Rotating the pentagon somewhere between its starting position and 18º might yield a larger area but you will have to get there by trial and error or defining the equation of the area with varying side lengths and finding the maximum area position.