A polygon inscribed in a circle, luckily, has a derived formula already. It is:
A = (nr²/2)[sin (360/n)]
where n is the number of sides of the polygon and r is the radius of the circle. For this problem, n = 100 and r = 1. Substituting this to the equation,
A = (100(1)²/2)[sin (360/100)]
A = 3.14 square units
Thus, the 100-gon has an area of 3.14 square units.