What is area?

Area is the amount of surface inside a flat (2D) shape. We measure area in square units, for example square centimetres (cm²), square metres (m²) or square kilometres (km²).

Remember: 100 cm = 1 m, so 1 m² = 10,000 cm².

Common formulas

• Rectangle: A = length × width (A = l × w)
• Square: A = side × side (A = s²)
• Triangle: A = 1/2 × base × height (A = ½ × b × h)
• Parallelogram: A = base × height (A = b × h)
• Trapezium (trapezoid): A = (a + b) / 2 × height
• Circle: A = π × radius² (A = πr²), use π ≈ 3.14 or 22/7

Visuals and examples

Worked examples (step-by-step)

Tips and common mistakes

• Always include units (e.g., m², cm²). Area is square units.
• Make sure the height you use is perpendicular (straight up) to the base.
• Convert lengths to the same unit before using a formula (e.g., cm to m).
• For triangles, the height may be inside the triangle or outside (use perpendicular height).

Practice questions (with answers)

1. Find the area of a rectangle 9 m by 7 m. (Answer: 63 m²)
2. A triangular plot has base 15 m and height 8 m. Area? (Answer: 60 m²)
3. A square tile has side 30 cm. Area of one tile? (Answer: 900 cm²)
4. A circle has diameter 14 m. Find the area (use π = 3.14). (Answer: r = 7 → A = 3.14 × 49 ≈ 153.86 m²)
5. A trapezium has parallel sides 5 m and 9 m and height 4 m. Area? (Answer: (5+9)/2 × 4 = 28 m²)

Quick checklist before you finish a question

• Are all lengths in the same unit?
• Did you use the correct formula for the shape?
• Is your final answer given with the correct square unit?