🏃 Perimeter Basics: Walking Around Shapes!

The Big Idea 💡

Imagine you have a beautiful garden, and you want to build a fence around it. How much fencing do you need? That’s perimeter!

Perimeter is like taking a walk around the edge of any shape and counting your steps.

🌟 What is Perimeter?

Perimeter = The total distance around a shape

Think of it like this:

• You’re an ant 🐜 walking along the edges of a cookie
• You start at one corner and walk ALL the way around
• When you get back to where you started, the total distance you walked is the perimeter!

Simple Example:

Imagine a square cookie 🍪
Each side is 4 cm

You walk: 4 + 4 + 4 + 4 = 16 cm

The perimeter is 16 cm!

Remember: Perimeter is always measured in length units (cm, m, inches, feet) — NOT square units!

📐 Perimeter of Polygons

A polygon is any shape with straight sides. Like triangles, squares, rectangles, pentagons, and more!

The Magic Formula:

Perimeter = Add up ALL the sides

That’s it! Just add every side together.

🔺 Triangle (3 sides)

graph TD
    A[Triangle] --> B[Add all 3 sides]
    B --> C[P = a + b + c]

Example: A triangle with sides 3 cm, 4 cm, and 5 cm:

P = 3 + 4 + 5 = 12 cm

⬜ Square (4 equal sides)

Since all sides are the same, there’s a shortcut!

P = 4 × side or P = side + side + side + side

Example: A square with side 5 m:

P = 4 × 5 = 20 m

OR the long way:
P = 5 + 5 + 5 + 5 = 20 m

📦 Rectangle (2 pairs of equal sides)

A rectangle has 2 long sides (length) and 2 short sides (width).

P = 2 × length + 2 × width

Or written as: P = 2(l + w)

Example: A rectangle with length 8 cm and width 3 cm:

P = 2 × 8 + 2 × 3
P = 16 + 6 = 22 cm

OR using the shortcut:
P = 2 × (8 + 3) = 2 × 11 = 22 cm

⬡ Any Polygon (Pentagon, Hexagon, etc.)

Just add all the sides! No special tricks needed.

Example - Pentagon (5 sides): Sides: 2, 3, 4, 3, 2 cm

P = 2 + 3 + 4 + 3 + 2 = 14 cm

⭕ Circumference: The Perimeter of a Circle!

Circles are special — they have NO straight sides!

So we give their perimeter a fancy name: Circumference

But wait… how do we measure around something with no sides to add up?

Here’s where the magic number Pi (π) comes in! 🎩✨

🥧 What is Pi (π)?

The Discovery Story:

Long ago, mathematicians wondered: “Is there a pattern in circles?”

They measured circles — big ones, small ones, pizza-sized, planet-sized!

They found something AMAZING:

When you divide the distance AROUND any circle by the distance ACROSS it…

You ALWAYS get the same number! 🤯

That number is Pi (π)

Pi’s Value:

π ≈ 3.14159…

But usually we just say: π ≈ 3.14

The cool part? Pi goes on FOREVER without repeating! It starts:

3.14159265358979323846...

For school and most calculations, just use 3.14 or the π button on your calculator.

Understanding the Parts of a Circle:

graph TD
    A[Circle Measurements] --> B[Diameter: d]
    A --> C[Radius: r]
    B --> D[Distance ACROSS the circle through center]
    C --> E[Distance from CENTER to EDGE]
    F[Key Relationship] --> G[d = 2 × r]

• Radius ® = from center to edge
• Diameter (d) = all the way across = 2 × radius

📏 Circumference Formulas

Formula 1: Using Diameter

C = π × d

Formula 2: Using Radius

C = 2 × π × r

Both give the same answer! Use whichever measurement you have.

Example 1: Finding Circumference with Diameter

A bicycle wheel has diameter 70 cm. What’s its circumference?

C = π × d
C = 3.14 × 70
C = 219.8 cm

Every time the wheel goes around once, it travels about 220 cm!

Example 2: Finding Circumference with Radius

A circular pizza has radius 15 cm. How much crust is around the edge?

C = 2 × π × r
C = 2 × 3.14 × 15
C = 6.28 × 15
C = 94.2 cm

That’s about 94 cm of delicious crust! 🍕

🎯 Quick Reference Summary

🧠 Remember This!

1. Perimeter = walk around the outside, add up the distance
2. Polygons = just add all sides together
3. Circumference = perimeter of a circle
4. Pi (π) = 3.14 = the magic circle number
5. Diameter = 2 × radius

🌈 Real Life Perimeter!

Where do we use perimeter?

• 🏠 Building a fence around your yard
• 🖼️ Putting a frame around a picture
• 🎁 Tying a ribbon around a gift box
• 🏃 Running around a track
• 🍪 Frosting the edge of a cookie

Every time you go AROUND something, you’re using perimeter!

Now you know how to measure the distance around ANY shape — straight sides or curvy! You’re a perimeter pro! 🏆