Types of Polygons Quiz

Types of Polygons

1. Definition of Polygons

   • A polygon is a closed, two-dimensional shape formed by a finite number of line segments (sides) that connect at vertices.

2. Classification by Number of Sides

   • Triangle (3 sides)
   • Quadrilateral (4 sides)
   • Pentagon (5 sides)
   • Hexagon (6 sides)
   • Heptagon (7 sides)
   • Octagon (8 sides)
   • Nonagon (9 sides)
   • Decagon (10 sides)
   • n-gon (n sides, where n is any number greater than 10)

3. Classification by Regularity

   • Regular Polygon
     • All sides and angles are equal.
     • Examples: Equilateral triangle, square.
   • Irregular Polygon
     • Sides and angles are not equal.
     • Examples: Scalene triangle, rectangle.

4. Classification by Convexity

   • Convex Polygon
     • All interior angles are less than 180°.
     • No sides are curved inward.
   • Concave Polygon
     • At least one interior angle is greater than 180°.
     • At least one vertex points inward.

5. Special Types of Polygons

   • Quadrilaterals include:
     • Trapezoid: At least one pair of parallel sides.
     • Parallelogram: Opposite sides are equal and parallel.
     • Rectangle: All angles are right angles; opposite sides are equal.
     • Rhombus: All sides are equal; opposite angles are equal.
     • Square: All sides and angles are equal.
   • Triangles include:
     • Equilateral: All sides and angles are equal.
     • Isosceles: Two sides are equal; two angles are equal.
     • Scalene: All sides and angles are different.
     • Right Triangle: One angle is 90°.

6. Properties of Polygons

   • The sum of the interior angles of a polygon can be calculated using the formula:
     • Sum = (n - 2) × 180°, where n is the number of sides.
   • The sum of the exterior angles of any polygon is always 360°.

7. Applications of Polygons

   • Used in geometry, architecture, computer graphics, and various fields of design.

Definition of Polygons

• A polygon is a closed two-dimensional figure made of a finite number of straight line segments, known as sides, which meet at points called vertices.

Classification by Number of Sides

• Triangle has 3 sides.
• Quadrilateral has 4 sides.
• Pentagon has 5 sides.
• Hexagon has 6 sides.
• Heptagon has 7 sides.
• Octagon has 8 sides.
• Nonagon has 9 sides.
• Decagon has 10 sides.
• General term n-gon applies to polygons with n sides, where n is any number greater than 10.

Classification by Regularity

• Regular Polygon: All sides and angles are equal; e.g., equilateral triangle and square.
• Irregular Polygon: Sides and angles are not uniform; e.g., scalene triangle and rectangle.

Classification by Convexity

• Convex Polygon: All interior angles are less than 180° and no sides curve inward.
• Concave Polygon: Contains at least one interior angle greater than 180° and at least one vertex points inward.

Special Types of Polygons

• Quadrilaterals:
  • Trapezoid: At least one pair of parallel sides.
  • Parallelogram: Opposite sides are equal and parallel.
  • Rectangle: All angles are right angles, and opposite sides are equal.
  • Rhombus: All sides are equal, and opposite angles are equal.
  • Square: All sides and angles are equal.
• Triangles:
  • Equilateral Triangle: All sides and angles are equal.
  • Isosceles Triangle: Two sides and angles are equal.
  • Scalene Triangle: All sides and angles are different.
  • Right Triangle: One angle measures 90°.

Properties of Polygons

• The interior angle sum of a polygon can be calculated using the formula: Sum = (n - 2) × 180°, where n represents the number of sides.
• The total of exterior angles in any polygon is always 360°.

Applications of Polygons

• Polygons play essential roles in geometry, architecture, computer graphics, and various design fields.