Area, Perimeter and Volume: Class 5 Study Guide
Measuring lets us describe how long, how big and how much a thing holds.
Perimeter is the distance around a flat shape. For a rectangle, perimeter = 2 × (length + breadth). A square with side 5 cm has a perimeter of 4 × 5 = 20 cm. Area is the amount of surface inside the shape. For a rectangle, area = length × breadth. A square with side 5 cm has an area of 5 × 5 = 25 square centimetres (cm²).
Volume is the space an object takes up. It is counted in cubic units. A box that is 3 cm long, 2 cm wide and 2 cm high holds 3 × 2 × 2 = 12 cubes of 1 cm³ each. Capacity is how much a container holds, measured in litres (L) and millilitres (mL).
Formulas to remember
| Shape | Perimeter | Area |
|---|---|---|
| Rectangle | 2 × (l + b) | l × b |
| Square | 4 × side | side × side |
| Cuboid volume | — | l × b × h |
Units and conversions
Choose a sensible unit and convert when needed. 1 m = 100 cm, 1 km = 1000 m, 1 kg = 1000 g, 1 L = 1000 mL. To change a larger unit to a smaller one, multiply: 2.5 m = 250 cm. To change a smaller unit to a larger one, divide: 3500 g = 3.5 kg.
| Quantity | Conversion | Example |
|---|---|---|
| Length | 1 m = 100 cm | 3 m = 300 cm |
| Distance | 1 km = 1000 m | 2.5 km = 2500 m |
| Mass | 1 kg = 1000 g | 4 kg = 4000 g |
| Capacity | 1 L = 1000 mL | 250 mL = 0.25 L |
Solving problems step by step
A rectangular garden is 12 m long and 8 m wide. How much fencing is needed, and what is the area for planting?
2 × (12 + 8) = 40 m of fencing.
12 × 8 = 96 m².
Fencing in metres, area in square metres.
Is 96 sensible for a garden that size?
Worked examples and common mistakes
Example: A tank 50 cm × 40 cm × 30 cm holds 50 × 40 × 30 = 60,000 cm³, which is 60 litres (1000 cm³ = 1 litre). Common mistakes: mixing up perimeter and area, writing cm instead of cm² and forgetting to convert units before calculating. Make sure all measurements are in the same unit first.
Check your understanding: model answers
1. Perimeter 26 cm; area 36 cm². 2. 2500 g. 3. 60 cm³.
✨ Key Takeaways
- Perimeter is around; area is inside.
- Area of a rectangle = l × b.
- Volume of a cuboid = l × b × h.
- Convert to the same unit before calculating.
💬 Questions for Discussion & Reflection
- Find the perimeter and area of a rectangle 9 cm by 4 cm.
- Convert 2.5 kg to grams.
- Find the volume of a box 5 cm × 4 cm × 3 cm.