Introduction to Polygons

Learn what polygons are and how to identify them by their sides and vertices.

Elementary20 minLesson
Printable worksheet

Definition

A polygon is a closed, flat shape made up of straight line segments called sides. The points where the sides meet are called vertices (singular: vertex).
Key features of a polygon:
  • It is a closed shape (no gaps or openings)
  • It has straight sides (no curves)
  • It is flat (two-dimensional)
Polygons are named by the number of sides:
SidesNameExample
3Triangle△\triangle
4QuadrilateralSquare, Rectangle
5Pentagon
6Hexagon
7Heptagon
8OctagonStop sign
10Decagon

Try it now

Which of these shapes is a polygon?

Worked Examples

Is this shape a polygon? A square with all sides equal.
1

Check if it's closed

The shape has no gaps - all sides connect → Yes, it's closed
2

Check if all sides are straight

All 4 sides are straight line segments → Yes, straight sides
3

Check if it's flat (2D)

The shape lies flat on a surface → Yes, it's flat
4

Count the sides and name it

4 sides = quadrilateral (specifically, a square) → 4-sided polygon

Common Mistakes

Thinking a circle is a polygon

Why it's wrong: A circle has no straight sides - it's one continuous curve.

Correct: Polygons must have straight sides. A circle is NOT a polygon.

Confusing vertices with sides

Why it's wrong: Vertices are the corner points; sides are the line segments.

Correct: Remember: Vertices (V) are points, Sides (S) are lines. A triangle has 3 of each.

Forgetting that polygons must be closed

Why it's wrong: An open shape (like the letter 'V') is not a polygon.

Correct: All sides must connect to form a complete, closed boundary.

Interactive Visual

Polygon explorer

12345

Sides

55

Vertices

55

Each interior angle (regular polygon)

(5−2)⋅180∘5=108∘\dfrac{(5 - 2) \cdot 180^\circ}{5} = 108^\circ

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

Practice Problems

16 problems
Problem 1 of 16
Easy
Which of these shapes is a polygon?

Why It Matters

Polygons are everywhere in our world:
  • Architecture: Buildings use triangular supports for strength, hexagonal tiles for floors
  • Nature: Honeycomb cells are hexagons, snowflakes often have six sides
  • Signs: Stop signs are octagons, yield signs are triangles
  • Sports: Soccer balls combine pentagons and hexagons
  • Art: Mosaics and patterns use polygons to create beautiful designs
Understanding polygons helps us describe, measure, and create shapes in the world around us!

Real World Applications

Road Signs

Traffic engineers use different polygon shapes to convey different messages at a glance.

Example:

A stop sign is an octagon (8 sides). Even if the word 'STOP' is covered, drivers recognize the shape.

1Try It Yourself

You're designing road signs. You need to identify polygons used in traffic.

A yield sign has 3 sides. What polygon is it?

Step 1: Choose the right answer

Name the polygon with 3 sides:

Honeycomb Architecture

Bees build honeycomb cells as hexagons because this shape uses the least wax while providing the most storage space.

Example:

Each cell in a honeycomb is a regular hexagon with 6 equal sides.

2Try It Yourself

You're studying a honeycomb pattern in science class.

If each hexagon cell has 6 sides, how many vertices does it have?

Step 1: Write the mathematical expression

Vertices in a hexagon:

Key Takeaways

  • 1A polygon is a closed, flat shape with straight sides
  • 2Vertices are the corner points where sides meet
  • 3The number of vertices equals the number of sides in any polygon
  • 4Polygons are named by their number of sides: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7), octagon (8)
  • 5A regular polygon has all sides equal and all angles equal

Frequently Asked Questions

No. A circle has no straight sides - it's made of one continuous curve. Polygons must have straight sides.
No. A circle has no straight sides - it's made of one continuous curve. Polygons must have straight sides.
A regular polygon has all sides equal length AND all angles equal. An irregular polygon has sides or angles of different sizes.
A triangle (3 sides) is the smallest polygon. You cannot make a closed shape with straight sides using fewer than 3 sides.

Glossary

Polygon
A closed, flat shape made of straight line segments
Vertex
A corner point where two sides of a polygon meet (plural: vertices)
Side
A straight line segment that forms part of the boundary of a polygon
Regular polygon
A polygon with all sides equal and all angles equal
Quadrilateral
A polygon with 4 sides (includes squares, rectangles, trapezoids)
Today's challengeOne problem, three tries

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