📐 Understanding Perimeter
Perimeter is the distance around the outside of a two-dimensional shape. Imagine you're building a fence around your yard; the total length of the fence is the perimeter.
- 📏 Definition: The total length of all the sides of a shape.
- ➕ Calculation: Add up the lengths of all the sides.
- 🧱 Example: For a rectangle with sides of 5 cm and 3 cm, the perimeter is $5 + 3 + 5 + 3 = 16$ cm.
⭕ Understanding Circumference
Circumference is a special type of perimeter that applies only to circles. It's the distance around the circle.
- 📍 Definition: The distance around a circle.
- ➗ Relationship to Diameter: The circumference is always a little more than three times the distance across the circle (the diameter).
- 🧮 Formula: Circumference ($C$) is calculated using the formula $C = \pi d$ or $C = 2 \pi r$, where $d$ is the diameter, $r$ is the radius, and $\pi$ (pi) is approximately 3.14159.
🤝 Key Differences
Here's a simple table summarizing the key differences:
| Feature |
Perimeter |
Circumference |
| Applies To |
Polygons (shapes with straight sides like squares, rectangles, triangles) |
Circles |
| Definition |
Distance around the outside of a shape |
Distance around the circle |
| Calculation |
Adding the lengths of all sides |
Using the formula $C = \pi d$ or $C = 2 \pi r$ |
✍️ Practice Problems
Let's test your understanding!
- 📐 Question 1: A square has sides of 7 cm each. What is its perimeter?
- ⭕ Question 2: A circle has a radius of 4 cm. What is its circumference? (Use $\pi = 3.14$)
- ➕ Question 3: A rectangle has a length of 10 cm and a width of 6 cm. What is its perimeter?
- ⏺️ Question 4: A circle has a diameter of 9 cm. What is its circumference? (Use $\pi = 3.14$)
- 🌳 Question 5: An equilateral triangle has sides of 5 cm each. What is its perimeter?
- ➗ Question 6: If the circumference of a circle is 31.4 cm, what is its approximate diameter? (Use $\pi = 3.14$)
- 📏 Question 7: A rectangular garden is 12 meters long and 8 meters wide. How much fencing is needed to enclose it?