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Overview

Regular Polygons

April 10, 2024
1 min read
polygon regular-polygon symmetry

What is a Regular Polygon?

A regular polygon is a closed figure where:

  1. All sides are equal in length.
  2. All angles are equal in measure.

Common examples include the equilateral triangle (3 sides), square (4 sides), regular pentagon (5 sides), and regular hexagon (6 sides).

General Formula for Perimeter

Since all sides are equal, we can find the perimeter by multiplying the number of sides by the length of one side.

Perimeter of Regular Polygon=(Number of sides)×(Length of one side)\text{Perimeter of Regular Polygon} = (\text{Number of sides}) \times (\text{Length of one side})

Examples

  1. Equilateral Triangle:
    • Sides: 3
    • Perimeter = 3×s3 \times s
  2. Square:
    • Sides: 4
    • Perimeter = 4×s4 \times s
  3. Regular Pentagon:
    • Sides: 5
    • Perimeter = 5×s5 \times s
  4. Regular Hexagon:
    • Sides: 6
    • Perimeter = 6×s6 \times s
Pentagon (5s)Hexagon (6s)

Split and Rejoin Concept

Sometimes, shapes can be cut and rearranged.

  • Key Insight: If you cut a shape and rearrange the pieces without overlap, the area remains the same, but the perimeter may change.

Example: A rectangle cut into two pieces and joined end-to-end creates a long, thin shape with a larger perimeter than the original compact rectangle.