What is the formula for the area of a regular polygon?

The formula for the area of a regular polygon is given by A = 1/2 * Perimeter * Apothem. This formula is particularly useful because it takes into account both the perimeter of the polygon and the apothem, which is the distance from the center of the polygon perpendicular to one of its sides.

In a regular polygon, all sides and angles are equal, allowing the apothem to serve as a reliable measurement for determining the area. The perimeter provides the total length around the polygon, and when you multiply the perimeter by the apothem, you get the total area covered. The factor of one-half comes into play because you are essentially forming a series of triangles with the apothem serving as a height from the center to each side of the polygon.

The other formulas relate to different shapes or contexts, such as the area of triangles or trapezoids, and do not directly apply to regular polygons. By using the formula involving the perimeter and the apothem, you are using an effective method that leverages the symmetrical properties of regular polygons to determine area accurately.