Polygons are closed flat shapes made from straight line segments, and their names often tell you how many sides they have. Learning polygon names helps students describe geometric figures clearly, compare shapes, and understand patterns in geometry. From triangles to decagons, the side count is the key feature used for naming.
This skill is important for classifying shapes, solving perimeter problems, and reading geometry diagrams accurately.
Many polygon names come from Greek number prefixes, such as tri for 3, penta for 5, and hexa for 6. A polygon can be regular, meaning all sides and all angles are equal, or irregular, meaning at least one side or angle is different. When a polygon has many sides or an unknown number of sides, mathematicians often call it an n-gon, where n represents the number of sides.
This notation makes it easy to write general formulas, such as the sum of interior angles of an n-gon.
Key Facts
- A polygon is a closed 2D figure made only of straight line segments.
- Number of sides = number of vertices = number of interior angles for any polygon.
- Triangle = 3 sides, quadrilateral = 4 sides, pentagon = 5 sides, hexagon = 6 sides.
- Heptagon = 7 sides, octagon = 8 sides, nonagon = 9 sides, decagon = 10 sides.
- A regular polygon has all sides congruent and all interior angles congruent.
- Sum of interior angles of an n-gon = (n - 2) × 180°.
Vocabulary
- Polygon
- A polygon is a closed two-dimensional shape made of three or more straight line segments.
- Side
- A side is one straight line segment that forms part of the boundary of a polygon.
- Vertex
- A vertex is a corner point where two sides of a polygon meet.
- Regular polygon
- A regular polygon is a polygon with all sides equal in length and all interior angles equal in measure.
- n-gon
- An n-gon is a polygon with n sides, where n is a number such as 6, 10, or 15.
Common Mistakes to Avoid
- Counting curved edges as polygon sides, which is wrong because polygons must be made only of straight line segments.
- Calling any four-sided shape a square, which is wrong because a square must have four equal sides and four right angles.
- Confusing side count with size, which is wrong because a small octagon still has 8 sides and a large triangle still has 3 sides.
- Assuming every pentagon or hexagon is regular, which is wrong because polygons can have the same number of sides but unequal side lengths or angles.
Practice Questions
- 1 A polygon has 9 sides. What is its name, and how many vertices does it have?
- 2 Find the sum of the interior angles of a 12-gon using the formula (n - 2) × 180°.
- 3 Two polygons both have 6 sides. One has all sides and angles equal, and the other does not. Explain how they can have the same name but different classifications.