Area — Grade 4 Mathematics
In Grade 4, we calculate the area of rectangles and introduce the formula for the area of a triangle: A = ½ × b × h. We also find areas of compound shapes by splitting or subtracting.
Area Formulas
Square: A = s²
Triangle: A = ½ × b × h
(where b = base, h = perpendicular height — the height at right angles to the base)
A = 12 × 7 = 84 cm²
A = ½ × b × h
Why ½ × b × h?
A triangle is exactly half of the rectangle with the same base and height. The rectangle's area is b × h, so the triangle's area is ½ × b × h.
Worked Examples
A triangle has base 14 cm and perpendicular height 9 cm. Find the area.
- A = ½ × b × h = ½ × 14 × 9
- = 7 × 9 = 63 cm²
A triangle has base 8 cm and area 28 cm². Find the perpendicular height.
- A = ½ × b × h → 28 = ½ × 8 × h = 4h
- h = 28 ÷ 4 = 7 cm
A shape is a rectangle (10 cm × 6 cm) with a triangle on top (base 10 cm, height 4 cm). Find the total area.
- Rectangle: 10 × 6 = 60 cm²
- Triangle: ½ × 10 × 4 = 20 cm²
- Total = 60 + 20 = 80 cm²
Practice Questions
1. Find the area of a triangle with base 10 cm and height 8 cm.
2. A triangle has area 45 cm² and base 9 cm. Find the height.
3. Find the area of a rectangle 13 cm long and 6 cm wide.
4. A square field has side 25 m. What is its area?
5. A shape is formed by a rectangle (8 m × 5 m) with a triangle cut out (base 4 m, height 3 m). Find the remaining area.
Key Points to Remember
- Area is measured in square units: cm², m², km².
- Rectangle: A = l × w; Triangle: A = ½ × b × h.
- The height (h) must be the perpendicular height — at right angles to the base.
- Compound shapes: split into simpler shapes, find each area, then add or subtract.
- Area and perimeter are different: perimeter is length (cm), area is space (cm²).