Area – Class 8 Mathematics notes, important questions and MCQs

Chapter overview

Area is the measure of the surface a figure covers. Formulas for basic shapes combine to find areas of complex shapes.

Formulas

• Rectangle l × b; square a²; triangle ½ × base × height.
• Parallelogram base × height; trapezium ½(a + b)h; rhombus ½ d₁d₂.
• Circle πr².

Composite figures and units

• Split into rectangles and triangles, then add (or subtract cut-outs).
• 1 m² = 10,000 cm²; 1 hectare = 10,000 m².

Key terms

Height

perpendicular distance from the base to the opposite vertex or side

Hectare

unit of land area equal to 10,000 m²

Trapezium area

½ × (sum of parallel sides) × distance between them

Formulas

• Trapezium = ½(sum of parallel sides) × height
• Rhombus = ½ d₁ d₂

Important questions with answers

Quick revision

• Triangle = half of rectangle with same base and height.
• 1 m² = 10,000 cm².
• Subtract the area of holes or paths when needed.

Exam tips

• Height must be perpendicular to the chosen base.
• Convert all lengths to the same unit before multiplying.

Practice MCQs

1. Area of a square of side 6 cm is

   1. 24 cm²
   2. 30 cm²
   3. 12 cm²
   4. 36 cm²
   Show answer

   Answer: (d) 36 cm². 6².

2. Area of a triangle with base 10 cm and height 6 cm is

   1. 60 cm²
   2. 16 cm²
   3. 30 cm²
   4. 15 cm²
   Show answer

   Answer: (c) 30 cm². ½ × 10 × 6.

3. Area of a trapezium with parallel sides 8 cm and 12 cm and height 5 cm is

   1. 50 cm²
   2. 100 cm²
   3. 40 cm²
   4. 60 cm²
   Show answer

   Answer: (a) 50 cm². ½ × 20 × 5.

4. 3 m² equals

   1. 300 cm²
   2. 3000 cm²
   3. 30,000 cm²
   4. 300,000 cm²
   Show answer

   Answer: (c) 30,000 cm². 3 × 10,000.

5. Area of a triangle with base 12 cm and height 7 cm is

   1. 84 cm²
   2. 38 cm²
   3. 19 cm²
   4. 42 cm²
   Show answer

   Answer: (d) 42 cm². ½ × 12 × 7.

6. A 20 m × 15 m garden has a 1 m wide path inside along its edges. Area of the path is

   1. 66 m²
   2. 70 m²
   3. 64 m²
   4. 74 m²
   Show answer

   Answer: (a) 66 m². 300 − (18 × 13) = 300 − 234 = 66.

7. A parallelogram has area 72 cm² and base 9 cm. Its height is

   1. 9 cm
   2. 6 cm
   3. 8 cm
   4. 12 cm
   Show answer

   Answer: (c) 8 cm. 72 ÷ 9.

8. 1 hectare equals

   1. 1,000 m²
   2. 100 m²
   3. 10,000 m²
   4. 1,00,000 m²
   Show answer

   Answer: (c) 10,000 m². 100 m × 100 m.