r cos (π/n) gives 1 cos(π/180) = 0.9998 for the measure of the apothem
Looking at a single wedge of the radially dissected polygon, split by the apothem, there is a right triangle with hypotenuse of 1 and leg of 0.9998. The third side (opposite the 1°) is sin 1° = x/1, so 0.0174. Double that to 0.0349 to get the side length.
Total perimeter is 6.28286632.
Now, to find the area of the wedge, we take the apothem times half the perimeter,
0.9998 * 3.14143316 = 3.14080487
(3.1408487 - π)/π = -0.0002368, so 0.023% error. Very close.
