The area of a regular polygon with 'n' sides and side length 'X' meters can be calculated using the following formula:
Area = [X²n] / [4tan(180°/n)]
Where:
* X is the length of one side of the polygon (in meters).
* n is the number of sides of the polygon.
* tan is the tangent trigonometric function.
This formula is derived by dividing the polygon into 'n' congruent triangles, and then using trigonometry to find the area of each triangle. The total area is the sum of the areas of these triangles.
Alternatively, if the apothem (the distance from the center of the polygon to the midpoint of a side) is known, the area can also be calculated as:
Area = (1/2) * apothem * perimeter
Where the perimeter is simply n * X.