📚 Class 7 CBSE – Mathematics
Perimeter & Area
1. What is Perimeter?
- Perimeter = the total length around a shape.
- Think of it as walking along the boundary of a field.
- It is measured in centimetres (cm), metres (m), or feet (ft).
Everyday Analogy
- Imagine you’re tying a string around a garden. The length of string you used = perimeter.
2. How to find the perimeter
| Shape | Formula | Example |
|---|---|---|
| Square | 4 × side | 4 × 6 cm = 24 cm |
| Rectangle | 2 × (length + breadth) | 2 × (8 cm + 3 cm) = 22 cm |
| Triangle | sum of all three sides | 5 cm + 7 cm + 9 cm = 21 cm |
| Circle | 2 × π × radius (≈ 3.14) | 2 × 3.14 × 4 cm ≈ 25.12 cm |
Tip: Always double‑check the units are the same before adding.
3. What is Area?
- Area = the amount of space inside a shape.
- Measured in square centimetres (cm²), square metres (m²), etc.
- Think of it as how many square tiles you would need to cover the floor.
4. How to find the area
| Shape | Formula | Example |
|---|---|---|
| Square | side² | 5 cm × 5 cm = 25 cm² |
| Rectangle | length × breadth | 7 cm × 4 cm = 28 cm² |
| Triangle | ½ × base × height | ½ × 6 cm × 5 cm = 15 cm² |
| Circle | π × radius² | 3.14 × 3 cm × 3 cm ≈ 28.26 cm² |
Quick Check: If you can draw a rectangle that exactly covers a shape, use that rectangle’s area.
5. Step‑by‑Step Tiny Example
Shape: Rectangle
- Length = 8 cm
- Breadth = 3 cm
| What to find | Calculation | Result |
|---|---|---|
| Perimeter | 2 × (8 + 3) | 2 × 11 = 22 cm |
| Area | 8 × 3 | 24 cm² |
6. Key Points to Remember
| Concept | Remember |
|---|---|
| Perimeter vs. Area | One is a line length (around), the other is a surface area (inside). |
| Units | Perimeter: linear units (cm, m). Area: squared units (cm², m²). |
| Shapes | Use the simplest formula for each shape. |
| π (pi) | Approximately 3.14. Use 3.14 for circles. |
| Always confirm units | Mixing cm and m can give wrong answers. |
7. Quick Practice Problems
| # | Shape | Given | Find |
|---|---|---|---|
| 1 | Square | side = 9 cm | Perimeter |
| 2 | Triangle | sides = 4 cm, 5 cm, 6 cm | Perimeter |
| 3 | Rectangle | length = 12 cm, breadth = 5 cm | Area |
| 4 | Triangle | base = 10 cm, height = 7 cm | Area |
| 5 | Circle | radius = 4 cm | Perimeter (circumference) |
8. Solutions to Practice Problems
| # | Result |
|---|---|
| 1 | 4 × 9 = 36 cm |
| 2 | 4 + 5 + 6 = 15 cm |
| 3 | 12 × 5 = 60 cm² |
| 4 | ½ × 10 × 7 = 35 cm² |
| 5 | 2 × 3.14 × 4 ≈ 25.12 cm |
9. Extra Tips
- Use a ruler for straight lines and a compass for circles.
- Sketch the shape before calculating; it helps to see the sides.
- Check your work by comparing with a known shape (e.g., a 5 cm square has 20 cm perimeter).
10. Summary
- Perimeter = total boundary length.
- Area = space inside the shape.
- Remember the basic formulas for squares, rectangles, triangles, and circles.
- Practice with small numbers; the steps stay the same for larger shapes.
Happy studying, and keep practicing! 🚀