Find the area of an inscribed 100-gon if the radius of the circle is 1 unit.

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.