Exercise Solutions Available
Step-by-step answers for all textbook questions in this chapter
Quick Summary
The Measurements chapter in Class 8 focuses on finding areas of special quadrilaterals (trapezium, rhombus) and computing surface areas and volumes of 3D solids (cube, cuboid). It is highly formula-based and appears in every term exam.
Key Formulae
| Shape / Solid | Formula |
|---|---|
| Area of trapezium | ½ × (a + b) × h |
| Area of rhombus | ½ × d₁ × d₂ |
| Perimeter of rhombus | 4 × side |
| Lateral surface area of cube | 4a² |
| Total surface area of cube | 6a² |
| Volume of cube | a³ |
| Lateral surface area of cuboid | 2h(l + b) |
| Total surface area of cuboid | 2(lb + bh + lh) |
| Volume of cuboid | l × b × h |
Area of a Trapezium
A trapezium has one pair of parallel sides (a and b) and a perpendicular height h between them.
Example: A trapezium has parallel sides 8 cm and 5 cm and height 4 cm. Area = ½ × (8 + 5) × 4 = ½ × 13 × 4 = 26 cm²
Area of a Rhombus
A rhombus has two diagonals d₁ and d₂ that bisect each other at right angles.
Example: Diagonals are 10 cm and 6 cm. Area = ½ × 10 × 6 = 30 cm²
Cube — Surface Area and Volume
A cube has all sides equal to length a.
- Total Surface Area = 6a²
- Volume = a³
Example: Cube with side 5 cm.
| TSA = 6 × 25 = 150 cm² | Volume = 125 cm³ |
|---|
Cuboid — Surface Area and Volume
A cuboid has length l, breadth b, and height h.
- Total Surface Area = 2(lb + bh + lh)
- Volume = l × b × h
Example: Cuboid 6 cm × 4 cm × 3 cm. TSA = 2(24 + 12 + 18) = 2 × 54 = 108 cm² Volume = 6 × 4 × 3 = 72 cm³
Important Questions
One Mark
- Write the formula for the area of a trapezium.
- A cube has side 3 cm. What is its volume?
- The diagonals of a rhombus are 12 cm and 8 cm. Find its area.
- What is the unit of volume?
- How many faces does a cuboid have?
Short Answer (3 marks)
- Find the area of a trapezium with parallel sides 10 cm and 6 cm, and height 5 cm.
- A cuboid is 8 m long, 5 m wide, and 3 m high. Find its total surface area and volume.
- The area of a rhombus is 60 cm² and one diagonal is 12 cm. Find the other diagonal.
Long Answer (5 marks)
- A room is 7 m long, 5 m wide, and 4 m high. Find the cost of painting the four walls and ceiling at ₹25 per m².
- A cuboidal tank 10 m × 6 m × 4 m is filled with water. How many litres of water does it hold? (1 m³ = 1000 litres)
Common Mistakes
- Using the slant side of a trapezium instead of the perpendicular height.
- Forgetting to halve the product of diagonals for rhombus area.
- Confusing lateral surface area (only 4 walls) with total surface area (all 6 faces).
Revision Checklist
- [ ] I know all formulae for trapezium, rhombus, cube, and cuboid.
- [ ] I can identify which formula to use from the information given.
- [ ] I have practised at least five word problems.
- [ ] I write correct units (cm², m², cm³, m³) in every answer.
- [ ] I have solved all textbook exercises and corrected mistakes.