Explanation
A polygon is a \(2D\) closed shape made of straight line segments.
To be a polygon, a shape must:
✔ Be closed
✔ Be made of straight lines
✔ Be two-dimensional (\(2D\))
Examples of polygons include:
- Triangle (\(3\) sides)
- Quadrilateral (\(4\) sides)
- Pentagon (\(5\) sides)
- Hexagon (\(6\) sides)
- Heptagon (\(7\) sides)
- Octagon (\(8\) sides)
Polygons can be classified in different ways.
A regular polygon has all sides equal and all angles equal.
An irregular polygon does not have all sides and angles equal.
In school-level geometry, we mainly study simple polygons, whose sides do not cross each other.
Shapes with curved sides, open shapes, and 3D objects are not polygons.
Formula / Rule
Conditions for a Polygon
A polygon must:
- be closed,
- be made of straight line segments,
- be two-dimensional.
Sum of Interior Angles
\((n−2)×180^{\circ}\)
where \(n\) is the number of sides.
Examples
Example 1
Is a triangle a polygon?
Yes.
It is:
- closed,
- made of straight sides,
- two-dimensional.
Therefore, a triangle is a polygon.
Example 2
Is a circle a polygon?
No.
A circle is made of a curve, not straight line segments.
Therefore, a circle is not a polygon.
Video Explanation
Practice
Continue Learning
- Polygons (Basics) (Current lesson)
- Types of Polygons
- Is this a Polygon