STORY OF THE POLYGON CLASS 8 NCERT QUADRILATERALS

 

📚 "The Tale of Polygons – Straight Lines, Sharp Minds!"

👋 Hello, I am Polygon – The Many-Sided Wonder!

Greetings, little mathematicians! I am Polygon, a closed figure made only with straight lines. You won’t find any curves or bends in me – I’m all sharp and precise.
My name comes from Greek: “poly” means many, and “gon” means angles. So yes – I’m the shape with many angles and sides!

🧾 My Definition: What Makes Me a Polygon?

To be part of my family, a shape must have:

  • Only straight sides (called line segments or edges)

  • A closed figure – no open ends

  • Each side connects to exactly two other sides at endpoints (called vertices)

  • No crossing or overlapping sides (for simple polygons)

🧩 How Many Types Am I?

Based on My Sides and Angles, I Come in Two Flavors:

1. Regular Polygon:

  • All sides are equal

  • All interior angles are equal

  • I’m the neatest one in the family!

  • Example: Equilateral triangle, square, regular hexagon

2. Irregular Polygon:

  • Sides and angles are not all equal

  • I love variety!

  • Example: Scalene triangle, trapezium

🔢 My Many Forms – I Grow With Every Side!

Number of Sides (n)NameInterior Angle SumEach Angle (if Regular)
3Triangle(3−2) × 180 = 180°60°
4Quadrilateral(4−2) × 180 = 360°90°
5Pentagon(5−2) × 180 = 540°108°
6Hexagon(6−2) × 180 = 720°120°
7Heptagon(7−2) × 180 = 900°~128.57°
8Octagon(8−2) × 180 = 1080°135°
9Nonagon(9−2) × 180 = 1260°140°
10Decagon(10−2) × 180 = 1440°144°

📐 My Angle Secrets

🔸 Interior Angle Sum Formula:

Sum = (n – 2) × 180°
(Where n is the number of sides)

🔹 Each Interior Angle (if Regular):

Each angle = [(n – 2) × 180°] ÷ n

🔸 Exterior Angle Sum:

No matter how many sides I have, if you go around me and measure one exterior angle at each vertex, the total is always:
360°

🎭 Meet My Famous Members

🔺 I’m Triangle – the smallest polygon

  • 3 sides, 3 angles

  • Total angle = 180°

  • I can be equilateral, isosceles, or scalene

  • I build strength into structures!

🔷 I’m Quadrilateral – four-sided, full of variety

  • Total angle = 360°

  • I include square, rectangle, rhombus, kite, and trapezium

🟠 I’m Pentagon – 5 sides

  • Angle sum = 540°

  • If regular, each angle is 108°

  • You’ll find me in nature (like in starfish)!

🔵 I’m Hexagon – honeybee’s favorite

  • 6 sides, angle sum = 720°

  • Each angle (if regular) = 120°

  • Found in beehives and snowflakes!

🟣 I’m Octagon – stop right there!

  • 8 sides, angle sum = 1080°

  • Found in traffic signs and designs

💡 Why I Matter

I’m not just a shape – I’m geometry's best friend. Architects, artists, engineers, and even nature uses me.
Whether in a tile floor, a soccer ball, a honeycomb, or a windowpane – I’m everywhere.

🌟 Polygon’s Final Words

"With every extra side, I grow stronger and more complex.
But I always follow the rule: be closed, be straight, and never bend.
I’m a polygon – proud, precise, and present in the world all around you!"


 

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HAPPY LEARNING

INSTITUTE OF THE CREATIVE SCIENCES, 9818541252.

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