AFOQT Practice Test

What is the area formula for a regular polygon?

1. 1/2ap

2. ap

3. ab

4. 2ap

The correct answer is: 1/2ap

The area formula for a regular polygon is primarily derived using the relationship between the apothem and the perimeter of the polygon. The correct formula is indeed given by multiplying the apothem (the distance from the center to the midpoint of a side) by the perimeter and then dividing by two. This can be expressed as: Area = (1/2) * ap This formula works because it effectively calculates the area by considering the polygon as composed of triangles that each have the apothem as one side. By summing the areas of these triangles over the entire perimeter of the polygon, you arrive at the area of the polygon itself. Other formulas provided in the choices either misrepresent the relationship between the apothem and perimeter or do not specifically relate to the area of a polygon so precisely. For example, simply multiplying the apothem by the perimeter without the factor of one-half does not account for the geometry of the triangles comprising the polygon. Understanding this connection is crucial for utilizing the area formula correctly in the context of regular polygons.