How do you find the area of a regular polygon?

To find the area of a regular polygon, the correct formula involves the perimeter and the apothem, which is the perpendicular distance from the center of the polygon to the midpoint of a side. The formula for the area of a regular polygon can be expressed as:

Area = (1/2) × perimeter × apothem

This makes sense because the perimeter gives the total length around the polygon, and the apothem provides the height necessary to convert that perimeter into an area. By multiplying the perimeter by the apothem and then taking half of that product, you effectively account for the triangular sections created between the center of the polygon and the edges. This method incorporates the symmetry and equal side lengths characteristic of regular polygons, ensuring an accurate area calculation.

The other options represent misunderstandings about how to compute the area of a polygon. For instance, simply using the base times height does not apply directly to polygons with more than four sides unless specifically defined. The notion of side length multiplied by the number of sides does not consider the shape and arrangement of the sides, and squaring the side length does not account for overall structure or dimensions needed for area computation.