Geometry Points: The Area of a Regular Polygon (Example 1)

To use the formula A = (1/2)ap to find the area of a regular polygon, you can follow these steps:

1. Identify the given information: Look for the measurements or information about the regular polygon that are already known or can be easily determined. These could be the apothem length (a) and the perimeter (p) of the polygon.

2. Understand the formula: The formula A = (1/2)ap represents the relationship between the area (A) of a regular polygon, its apothem length (a), and its perimeter (p). In this formula, the apothem is the distance from the center of the polygon to the midpoint of any side.

3. Substitute the known values: Once you have identified the apothem length (a) and the perimeter (p) of the regular polygon, substitute these values into the formula A = (1/2)ap.

4. Calculate the area: Multiply the apothem length (a) by the perimeter (p), and then divide the result by 2. The result will be the area (A) of the regular polygon.

By following these steps and applying the formula A = (1/2)ap, you can determine the area of a regular polygon using the given apothem length and perimeter. It's worth noting that the apothem length is the key value to find the area of a regular polygon, as it represents the distance from the center to the midpoint of any side.

These videos are designed to review and reteach high school Geometry content. My videos cover…

Points, Lines, and Planes,
Angles and Angle Relationships,
Triangles,
Quadrilaterals,
Circles,
Similarity and Proportions,
Congruent Figures,
Coordinate Geometry,
Transformations,
Area and Perimeter,
Volume and Surface Area,
Right Triangles and Trigonometry,
Geometric Proofs,
Constructions,
Non-Euclidean Geometries.

Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa
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