Irregular polygon

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

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

What is an irregular polygon?

An irregular polygon is a polygon that does not have all its sides equal. It also has unequal angle measurements. If a polygon has all equal sides and interior angles, it is a regular type of polygon.

For example,

Regular pentagon:	Irregular pentagon:
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 irregular polygons,

Polygon	Number of sides/vertices	Image
Scalene triangle	\textbf{3}
Irregular quadrilateral	\textbf{4}
Irregular pentagon	\textbf{5}
Irregular hexagon	\textbf{6}
Irregular octagon	\textbf{8}

What are irregular 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 (for 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 an irregular polygon

In order to classify an irregular polygon:

1. Check to see that the polygon has different size angles or sides.
2. Count the number of sides of the polygon.
3. Name the polygon based on the number of sides.

Irregular polygon examples

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

Name the shape.

1. Check to see that the polygon has different size angles or sides.

There are sides and angles that are not congruent (equal), so the polygon is irregular.

2Count the number of sides of the polygon.

There are 4 sides.

3Name the polygon based on the number of sides.

The polygon is an irregular quadrilateral.

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

Name the shape.

Check to see that the polygon has different size angles or sides.

There are sides and angles that are not congruent, so the polygon is irregular.

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 different size angles or sides.

There are sides and angles that are not congruent, so the polygon is irregular.

Notice that some angles and sides are congruent, but since not all angles and sides are, the figure is irregular.

Count the number of sides of the polygon.

There are 8 sides.

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

Name the shape.

Check to see that the polygon has different size angles or sides.

There are sides and angles that are not congruent, so the polygon is irregular.

Notice that 2 angles are congruent, but since not all angles are, the figure is irregular.

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 different size angles or sides.

There are sides and angles that are not congruent, so the polygon is irregular.

Count the number of sides of the polygon.

There are 6 sides.

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

Name the shape.

Check to see that the polygon has different size angles or sides.

There are sides and angles that are not congruent, so the polygon is irregular.

Count the number of sides of the polygon.

There are 6 sides.

Teaching tips for irregular polygons

• Worksheets can be a good way for students to practice identifying irregular polygons, but it is also important for students to work with shapes in real life. One way to do this is to give students straws that are of different lengths and clay. They can use the straws as line segments and connect them with clay to create irregular polygons.
  
  Once students have created an irregular polygon, they can compare and contrast their polygon with what other students have made, or if they are working on their own, they can draw a picture of it and then create another polygon with the same number of sides, but a different overall shape.

• Highlight irregular polygons that are common in everyday life (at home or at school) and encourage students to notice them as well. Even if they don’t know how to classify a polygon, just naming a shape that is an irregular polygon helps form meaning around this topic.

Easy mistakes to make

• Thinking that irregular polygons can’t have any equal sides or angles
  An irregular polygon can have some equal sides and angles.
  For example,
  

  

  This irregular hexagon does have some equal sides and angles, but they are not ALL equal, so it is irregular. A rhombus is a quadrilateral with four equal sides, however, not all of its angles are equal, therefore a rhombus is not a regular quadrilateral – that is a square.

• Thinking only regular polygons are polygons
  Many children’s books, classroom posters, and other commonly used objects show only regular polygons. This makes it easy for students to think that a shape has to be in these exact forms.
  

  

  For example,
  Thinking a 6 sided closed figure is not a hexagon, because it does not look like a regular hexagon.
  Seeing and talking about irregular polygons helps correct this misconception.

• Incorrect quadrilateral classification
  There are many irregular quadrilaterals and it is common to confuse the properties, especially for a rhombus, parallelogram, or trapezoid. When asked to specify the classification of an irregular quadrilateral, always recall the qualities of each type.

Related 2D shape lessons

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

The next lessons are

• Quadrilateral
• Triangles
• Perimeter
• Area of the triangle
• Isosceles triangle

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