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PolygonsHere 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.

An** irregular polygon** is a closed, straight-sided figure that has **unequal sides or 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} |

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.

In order to classify an irregular polygon:

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

Assess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!

DOWNLOAD FREEAssess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!

DOWNLOAD FREEName the shape.

**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.

2**Count the number of sides of the polygon.**

There are 4 sides.

3**Name the polygon based on the number of sides.**

The polygon is an irregular quadrilateral.

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.

**Name the polygon based on the number of sides.**

The polygon is an irregular triangle. More specifically, it is also a right scalene triangle.

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.

**Name the polygon based on the number of sides.**

The polygon is an irregular octagon.

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.

**Name the polygon based on the number of sides.**

The polygon is an irregular pentagon.

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.

**Name the polygon based on the number of sides.**

The polygon is an irregular hexagon.

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.

**Name the polygon based on the number of sides.**

The polygon is an irregular hexagon.

- 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.

**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.

- 2D shapes
- Regular polygon
- Symmetry
- Lines of symmetry
- Hexagon shape
- How to draw a hexagon
- Pentagon
- Octagon

1. Which of the following is an irregular polygon?

Irregular polygons are closed, straight sided figures that have unequal sides and angles.

The figure is closed, made up of straight sides and has unequal sides and angles.

2. Which of the following is an irregular polygon?

Irregular polygons are closed, straight sided figures that have unequal sides and angles.

The figure is closed, straight sided and has unequal sides and angles.

Even though it has some equal sides and angles, because ALL the sides and angles are not equal, it is irregular.

3. Which of the following is an irregular hexagon?

An irregular hexagon is a 6 sided closed figure that has unequal sides and angles.

The figure is closed and has unequal sides and angles.

Even though it has some equal sides and angles, because ALL the sides and angles are not equal, it is irregular.

4. Which of the following is an irregular quadrilateral?

An irregular quadrilateral is a 4 sided closed figure that has unequal sides or angles.

The figure is closed and has unequal sides or angles.

Even though it has some equal sides and angles, because ALL the sides and angles are not equal, it is irregular.

5. What is the name of the figure?

irregular hexagon

octagon

quadrilateral

irregular pentagon

An irregular pentagon is a 5 sided closed figure that has unequal sides and angles.

6. What is the name of the figure?

irregular octagon

irregular hexagon

pentagon

irregular triangle

An irregular octagon is an 8 sided closed figure that has unequal sides and angles.

Just like the interior angles of a polygon, the exterior angles of regular polygons are all congruent and for irregular polygons they are not all congruent.

Yes, you break the shape up into common shapes that have an area formula, such as rectangles and triangles. Then you find the area of each part and add all the parts together to find the total area.

A concave polygon has one or more interior angles that are greater than 180 degrees. A convex polygon has interior angles that are all less than 180 degrees.

A polygon with equal side lengths and equal angles. An example is an equilateral triangle.

- Quadrilateral
- Triangles
- Area of the polygon
- Area of the triangle
- Isosceles triangle

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