Polygon Concepts: Apothem

Polygons

Definition

The apothem of a regular polygon is the perpendicular distance from the center of the polygon to the midpoint of one of its sides.

Description

In geometry, the apothem is a crucial element for understanding regular polygons, which are polygons with all sides and angles equal. The apothem serves as a key component in various geometric calculations, particularly in determining the area of regular polygons. The formula for the area of a regular polygon is given by:

$$A = \frac{1}{2} \cdot a \cdot P$$

where A is the area, a is the apothem, and P is the perimeter of the polygon. This formula highlights the importance of the apothem in simplifying complex area calculations. The apothem also relates to the radius of the polygon's incircle, providing further geometric insights. Understanding the apothem is fundamental for students and professionals working with geometric shapes, as it connects various properties and measures within regular polygons.

For a complete collection of terms related to polygons click on this link: Polygons Collection.

Common Core Standards CCSS.MATH.CONTENT.5.G.B.3, CCSS.MATH.CONTENT.5.G.B.4, CCSS.MATH.CONTENT.3.G.A.1, CCSS.MATH.CONTENT.3.MD.D.8, CCSS.MATH.CONTENT.6.G.A.1, CCSS.MATH.CONTENT.6.G.A.3, CCSS.MATH.CONTENT.HSG.CO.A.3 3 - 8 Geometry     • Polygons         • Definition of a Polygon 2021 polygon, definitions, glossary term