Difference between the areas of the circumcircle and the incircle of an n-sided regular polygon

Question:

To find the difference between the areas of the circumcircle and the incircle of an n-sided regular polygon.

Solution:

Result:

The difference between the areas of the circumcircle and the incircle of an n sided regular polygon is pi times square of the length of the side divided by 4.

Note:

The difference between the areas of the circumcircle and the incircle of an n-sided regular polygon is independent of the number of sides. It depends only on the length of the side.

© Rishabh Bidya