Classifying Polygons

Learn to identify and classify polygons by their number of sides and angles.

Elementary20 minLesson
Printable worksheet

Definition

A polygon is a closed, flat shape made of straight line segments called sides. We classify polygons by counting their sides:
SidesNameExample
3TriangleStop yield signs
4QuadrilateralWindows, doors
5PentagonThe Pentagon building
6HexagonHoneycomb cells
7HeptagonSome coins
8OctagonStop signs
9NonagonNine-sided shapes
10DecagonTen-sided shapes
Key rule: The number of sides always equals the number of angles (vertices).

Try it now

Which shape is a polygon?

Worked Examples

A shape has 5 straight sides. What type of polygon is it?
1

Count the sides

The shape has 5 sides
2

Use the naming rule

Penta- means 5, -gon means angles/sides → Pentagon
3

Verify

A pentagon has 5 sides and 5 angles → Confirmed: Pentagon

Common Mistakes

Confusing quadrilateral with rectangle

Why it's wrong: A quadrilateral is ANY 4-sided polygon. Rectangles, squares, trapezoids, and rhombuses are all quadrilaterals.

Correct: Quadrilateral is the general name for all 4-sided shapes. Rectangle is a specific type of quadrilateral.

Thinking circles are polygons

Why it's wrong: Circles have no straight sides or angles. Polygons must have straight line segments.

Correct: Polygons are made of straight lines only. Circles are curved shapes, not polygons.

Forgetting that sides = angles

Why it's wrong: Every side meets another side at a vertex, creating an angle.

Correct: A polygon with nn sides always has exactly nn angles (vertices).

Interactive Visual

Polygon explorer

123456

Sides

66

Vertices

66

Each interior angle (regular polygon)

(6−2)⋅180∘6=120∘\dfrac{(6 - 2) \cdot 180^\circ}{6} = 120^\circ

Move the slider: a polygon always has as many vertices as sides.

Practice Problems

15 problems
Problem 1 of 15
Easy
Which shape is a polygon?

Why It Matters

Polygons are everywhere in our world! Understanding how to classify them helps you:
  • Architecture: Builders use polygon knowledge to design stable structures
  • Nature: Honeybees build hexagonal cells because hexagons fit together perfectly
  • Art & Design: Artists use different polygons to create patterns and tessellations
  • Road Safety: Traffic signs use specific polygon shapes (octagons for STOP, triangles for YIELD)
When you can name and classify polygons, you see geometry all around you!

Real World Applications

Traffic Signs

Road signs use specific polygon shapes to communicate meaning quickly.

Example:

STOP signs are octagons (8 sides), YIELD signs are triangles (3 sides), and speed limit signs are rectangles (4 sides).

1Try It Yourself

You see a road sign shaped like a regular polygon with 8 sides.

What type of polygon is this sign, and what does it likely say?

Step 1: Choose the right answer

An 8-sided polygon is called a(n):

Nature's Geometry

Honeybees build hexagonal cells in their hives because hexagons tessellate perfectly.

Example:

Each honeycomb cell is a hexagon (6 sides). Hexagons fit together with no gaps, maximizing storage space.

2Try It Yourself

You examine a honeycomb and count the sides of one cell.

What polygon is each cell, and why do bees choose this shape?

Step 1: Choose the right answer

A 6-sided polygon is a:

Sports Fields

Many sports use polygon-shaped fields and equipment.

Example:

A soccer ball has pentagons (5 sides) and hexagons (6 sides). Baseball's home plate is a pentagon.

3Try It Yourself

Baseball's home plate has 5 sides.

What type of polygon is home plate?

Step 1: Choose the right answer

A 5-sided polygon is a:

Key Takeaways

  • 1Polygons are closed shapes made of straight line segments (sides)
  • 2We classify polygons by counting their sides: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7), octagon (8)
  • 3The number of sides always equals the number of angles
  • 4Regular polygons have all sides equal AND all angles equal
  • 5Polygons appear everywhere: signs, buildings, nature, sports equipment

Frequently Asked Questions

A polygon is a specific type of shape: closed, flat, with straight sides only. Circles, ovals, and curved shapes are not polygons.
A polygon is a specific type of shape: closed, flat, with straight sides only. Circles, ovals, and curved shapes are not polygons.
Yes! A square is a special rectangle where all four sides are equal. All squares are rectangles, but not all rectangles are squares.
Polygons can have any number of sides! A 12-sided polygon is a dodecagon, a 20-sided is an icosagon. As sides increase, the polygon looks more like a circle.

Glossary

Polygon
A closed, flat shape made of straight line segments
Regular polygon
A polygon where all sides are equal length and all angles are equal
Irregular polygon
A polygon where sides and/or angles are not all equal
Vertex
A corner point where two sides of a polygon meet (plural: vertices)
Quadrilateral
Any polygon with exactly 4 sides
Tessellate
To fit together in a pattern with no gaps or overlaps
Today's challengeOne problem, three tries

More in This Topic

Introduction to Polygons

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Diagonals of Polygons

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Polygon Angle Sum Formula

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Exterior Angles of Polygons

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