Introduction Have you ever looked at a stop sign, a tiled floor, or a honeycomb and wondered what all these shapes have in common? They’re polygons! Polygons are all around us—in buildings, art, nature, and even in video games! In this blog post, we’ll explore what polygons are, how many types exist, how to calculate angles and area, and where we see them in real life. Ready? Let’s dive into the exciting world of polygons! 🔷 What Is a Polygon? A polygon is a closed 2D shape made by straight lines. These lines are called sides, and they connect to form a closed figure. A polygon must have at least three sides. 👉 Key Points: Closed shape: It starts and ends at the same point. Straight lines: No curves. At least 3 sides: A shape with fewer than 3 sides isn’t a polygon. ✏️ Examples of polygons: Triangle (3 sides) Square or rectangle (4 sides) Pentagon (5 sides) Hexagon (6 sides) Octagon (8 sides) ❌ Not polygons: A circle (it has no straight sides) An open figure (not closed) A shape with curved lines 🧩 Parts of a Polygon Let’s understand the important parts of a polygon: Sides – The straight lines that make up the shape. Vertices – The corners or points where the sides meet. Angles – Formed where two sides meet. Example: A triangle has 3 sides, 3 angles, and 3 vertices. 🏷️ Names of Polygons (Based on the Number of Sides) Sides Name 3 Triangle 4 Quadrilateral (Square, Rectangle) 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon You can use the word “n-gon” for any number of sides. For example, a shape with 12 sides is a 12-gon. 🧠 Types of Polygons 1. Regular and Irregular Polygons Regular Polygon: All sides and angles are equal. Example: An equilateral triangle or a square. Irregular Polygon: Sides and angles are not equal. Example: A scalene triangle. 2. Convex and Concave Polygons Convex: All angles are less than 180°. It “bulges out”. Concave: One or more angles are greater than 180°. It “caves in”. 3. Simple and Complex Polygons Simple: Sides do not cross each other. Complex: Sides cross over each other (like a star). 🔢 Interior and Exterior Angles 🔸 Interior Angles Interior angles are the angles inside the polygon. To find the sum of all interior angles: Sum = ( � − 2 ) × 180 ∘ Sum=(n−2)×180 ∘ Where � n is the number of sides. Polygon Formula Sum of Angles Triangle (3 − 2) × 180 180° Quadrilateral (4 − 2) × 180 360° Pentagon (5 − 2) × 180 540° Hexagon (6 − 2) × 180 720° 🔸 Exterior Angles The sum of all exterior angles of any polygon is always: 360 ∘ 360 ∘ Each exterior angle in a regular polygon: = 360 ∘ � = n 360 ∘ ​ 📏 Area and Perimeter Perimeter: The perimeter is the total length around the polygon. Perimeter = sum of all sides Perimeter=sum of all sides Area: To find the area, we need different formulas for different polygons. Triangle: Area = 1 2 × base × height Area= 2 1 ​ ×base×height Square: Area = side 2 Area=side 2 Rectangle: Area = length × breadth Area=le

1. Introduction to Polygons and Angle Properties

2. What is a Polygon?
 A closed figure made up of straight lines
 Must be closed with no gaps
 Lines must be straight (not curved)
 Examples: triangles, squares, pentagons
 Real-world examples: stop signs, picture frames, tiles

3. Regular vs. Irregular Polygons
 Regular polygons:
• All sides are equal in length
• All angles are equal in measure
• Examples: square, equilateral triangle
 Irregular polygons:
• Sides and angles may be different
• Example: rectangle (equal angles but different side lengths)

4. Parts of a Polygon
 Vertices: Points where sides meet
 Sides: Straight lines connecting vertices
 Interior angles: Angles inside the polygon
 Exterior angles: Angles outside at each vertex
 Diagonal: Line connecting non-adjacent vertices

5. Understanding Quadrilaterals
 4-sided polygons
 Sum of interior angles = (360°)
 Types include:
• Squares
• Rectangles
• Rhombuses
• Trapezoids
• Parallelograms

6. The Angle Sum Formula
 For any polygon with n sides:
 Sum of interior angles = (n-2) × 180°
 Example: Pentagon (5 sides)
• n = 5
• (5-2) × 180° = 540°

7. Let's Practice!
 Find the sum of interior angles:
• Hexagon (6 sides):
 (6-2) × 180° = 720°
• Octagon (8 sides):
 (8-2) × 180° = 1080°

8. Real-World Applications
 Architecture: Building design
 Floor tiling patterns
 Sports field layouts
 Traffic signs
 Art and design
 Construction and engineering

9. Common Mistakes to Avoid
 Remember: curves aren't part of polygons
 Don't forget to close the shape
 Count sides carefully when using the formula
 Double-check your calculations
 Make sure angles add up correctly

10. Review Questions
 What makes a polygon regular?
 What's the sum of angles in a pentagon?
 How many diagonals can you draw in a square?
 Why is a circle not a polygon?
 Calculate the sum of angles in a 7-sided polygon