Question

Find the area An of an n-sided regular polygon inscribed in a circle of radius 1.

Answer 1

A≈3.14

Answer 2

Consider a square as an example, so \(n=4\) (much easier to draw than a 10+ -gon):

You can cut up the square into triangles and figure out the length of the side and apothem, then use the area formula:
\[A=\frac{ap}{2}\]
where \(a\) is the apothem and \(p\) is the perimeter.