Finding a general formula that calculates the area of any n-point star enclosed in a r radius circle (example below)

[Tendon]

Finding a general formula that calculates the area of any n-point star enclosed in a r radius circle (example below)

Here is the example of the 5-point star.

 

[Dr.Peterson]

Here is the example of the 5-point star.

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I presume, if you have put any effort into this, that you have discovered that it takes more than just one number n to describe such a polygon: https://mathworld.wolfram.com/StarPolygon.html

Also, how are you defining its area? That can be interpreted in different ways: https://en.wikipedia.org/wiki/Star_polygon#Interiors