Polygons • Topic 1 of 3

Types of Polygons and Their Properties

What is a Polygon? A polygon is a closed two-dimensional figure formed by three or more straight line segments. The word comes from Greek: "poly" means many and "gon" means angles.

Classification of Polygons by Number of Sides:

Number of SidesNameExample
3TriangleThree-sided figure
4QuadrilateralSquare, rectangle
5PentagonFive-sided figure
6HexagonSix-sided figure
7HeptagonSeven-sided figure
8OctagonEight-sided figure
9NonagonNine-sided figure
10DecagonTen-sided figure

Types of Polygons based on Shape:

TypeDescription
Convex polygonAll interior angles < 180°, all diagonals lie inside
Concave polygonAt least one interior angle > 180°, at least one diagonal lies outside
Regular polygonAll sides equal AND all angles equal
Irregular polygonSides and/or angles are not all equal

Key Properties of Polygons:

  • A polygon has the same number of sides, vertices, and interior angles
  • The sum of exterior angles of any polygon is always 360°
  • A diagonal is a line segment joining two non-adjacent vertices
Polygons — Types and Names3Triangle4Quadrilateral5Pentagon6Hexagon8OctagonInterior Angle Sum of n-sided polygon = (n − 2) × 180°Each interior angle of a REGULAR polygon = (n−2) × 180° ÷ n
Solved Examples
1
Worked Example
Name the polygon with: (a) 6 sides (b) 8 sides (c) 5 sides
Solution- (a) 6 sides → Hexagon - (b) 8 sides → Octagon - (c) 5 sides → Pentagon - **Answer:** (a) Hexagon, (b) Octagon, (c) Pentagon *Example 2: Classify the following as convex or concave: A polygon where one interior angle is 210°. Solution: - If an interior angle is greater than 180°, the polygon is concave - 210° > 180°, so the polygon is concave - **Answer:** Concave polygon *Example 3: How many diagonals does a pentagon have? Solution: - Pentagon has 5 vertices - Total line segments between vertices = \(\frac{5 \times 4}{2} = 10\) - Subtract the 5 sides = \(10 - 5 = 5\) diagonals - **Answer:** 5 diagonals

Key Points

  • A polygon is a closed figure with straight sides
  • Polygons are named by number of sides: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), etc.
  • Convex: all interior angles < 180°
  • Concave: at least one interior angle > 180°
  • Regular: all sides and all angles equal
  • Number of diagonals = \(\frac{n(n-3)}{2}\) where \(n\) = number of sides
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Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.A polygon is a closed figure made of:
Explanation: Line segments.
Q2.A pentagon has how many sides?
Explanation: Five.
Q3.A hexagon has how many sides?
Explanation: Six.
Q4.A polygon with all sides and angles equal is:
Explanation: Regular.
Practice more MCQs → 📝 Assignment · 35 marks