To find the area of a regular 20-gon, we can use the formula for the area of a regular polygon:
A = (1/2) * a * p
Where "A" is the area of the polygon, "a" is the length of the side, and "p" is the apothem. In this case, we are given that the side length is 24 nm and the apothem is 75.8. Plugging these values into the formula, we get:
A = (1/2) * 24 * 75.8
Solving for the area, we get:
A = 927.2
Therefore, the area of the regular 20-gon is 927.2 nm^2.