Regular polygon

Here you will learn about regular polygons, including what they are and how to classify them.

Students will first learn about regular polygons as part of geometry in 2nd grade and 3rd grade.

What is a regular polygon?

A regular polygon is a closed, straight-sided figure that has equal side and angle measurements. If a polygon does not have all equal sides and interior angles, it is an irregular polygon.

For example,

Regular quadrilateral:	Irregular quadrilateral:
All the sides are the same length.	All the sides are NOT the same length.
All the angles are the same size	All the angles are NOT the same size

The table below gives examples of regular polygons:

Polygon	Number of sides/vertices	Image (regular polygon)
Equilateral triangle	3
Square (quadrilateral)	4
Regular pentagon	5
Regular hexagon	6
Regular octagon	8

What are regular polygons?

Common Core State Standards

How does this relate to 2nd grade math and 3rd grade math?

• Grade 2 – Geometry (2.G.A.1)
  Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

• Grade 3 – Geometry (3.G.A.1)
  Understand that shapes in different categories (example, rhombuses, rectangles, and others) may share attributes (example, having four sides), and that the shared attributes can define a larger category (example, quadrilaterals).
  
  Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

How to classify a regular polygon

In order to classify a regular polygon:

1. Check to see that the polygon has congruent (equal) angles and sides.
2. Count the number of sides of the polygon.
3. Name the polygon based on the number of sides.

Regular polygon examples

Example 1: classify the shape – by sides and regular or irregular

Name the shape.

1.  Check to see that the polygon has congruent (equal) angles and sides.

All the sides and angles are congruent, so the polygon is regular.

2Count the number of sides of the polygon.

There are 4 sides.

3Name the polygon based on the number of sides.

The polygon is a regular quadrilateral or more specifically a square.

Example 2: classify the shape – by sides and regular or irregular

Name the shape.

Check to see that the polygon has congruent (equal) angles and sides.

All the sides and angles are congruent, so the polygon is regular.

Count the number of sides of the polygon.

There are 3 sides.

Example 3: classify the shape – by sides and regular or irregular

Name the shape.

Check to see that the polygon has congruent (equal) angles and sides.

All the sides and angles are congruent, so the polygon is regular.

Count the number of sides of the polygon.

There are 6 sides.

Example 4: classify the shape – by sides and regular or irregular

Name the shape.

Check to see that the polygon has congruent (equal) angles and sides.

All the sides and angles are congruent, so the polygon is regular.

Count the number of sides of the polygon.

There are 5 sides.

Example 5: classify the shape – by sides and regular or irregular

Name the shape.

Check to see that the polygon has congruent (equal) angles and sides.

All the sides and angles are congruent, so the polygon is regular.

Count the number of sides of the polygon.

There are 8 sides.

Example 6: classify the shape – by sides and regular or irregular

Name the shape.

Check to see that the polygon has congruent (equal) angles and sides.

All the sides and angles are congruent, so the polygon is regular.

Count the number of sides of the polygon.

There are 4 sides.

Teaching tips for regular polygons

• Give students opportunities to physically create regular polygons, not just draw or identify them. A simple activity with straws of the same lengths and clay can be used. Identify the straws as line segments and the clay as vertices. Then students can use them to create their own regular polygons.

• Instead of emphasizing quizzes, routinely highlight regular polygons that are common in everyday life (at home or at school) and encourage students to notice them as well. Daily practice over time helps students remember the definitions and also provides them with a variety of real life examples for each regular polygon.

Easy mistakes to make

• Thinking a rectangle is a regular polygon
  Since the sides of a regular polygon must be equal, a rectangle is not a regular polygon unless it has 4 equal sides – which is more specifically classified as a square.
  For example,
  

  

• Thinking regular polygons can’t have diagonal lines
  While polygons must have straight sides, the sides don’t have to be vertical (go up and down). They can also be diagonal (on a slant), such as in a regular triangle or pentagon.
  For example,
  
  

  

Related 2D shape lessons

• 2D shapes
• Irregular polygon
• Polygons
• Hexagon shape
• How to draw a hexagon
• Pentagon shape
• Octagon shape

The next lessons are

• Quadrilateral
• Triangles
• Perimeter

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