Min Area of Regular Polygon

Consider a regular polygon with n sides, where the length of each side is denoted as s. In addition, imagine that this polygon is inscribed in a circle, referred to as the circumcircle, with a radius R.

For a regular polygon, the formula for the area A can be expressed in terms of the number of sides and the circumradius as follows:

$$ A = \f\frac{1}{2} n R^2 \sin\left(\f\frac{2\pi}{n}\right) $$

The problem requires you to find the minimum value of the area of a regular polygon where the number of sides n takes values from 5 to 12. Assume that the circumradius R is constant and equal to 1. Which of the following polygons has the minimum area?