Four area formulas
The area of a shape is the amount of flat surface it covers, measured in square units such as cm² or m². Each of these shapes has a formula that uses a base and a perpendicular height, or the diagonals.
Key idea / 要点
Triangle: A = ½ × base × height.
Parallelogram: A = base × height.
Kite: A = ½ × d₁ × d₂ (the two diagonals).
Trapezium: A = ½ × (a + b) × height, where a and b are the two parallel sides.
The height is always the perpendicular distance — measured at a right angle to the base — not the slanted side. A common mistake is to multiply the two slanted sides of a parallelogram; instead, always pair the base with the height drawn straight across to the opposite side. For a kite and a trapezium, notice that both formulas begin with ½, just like the triangle.
Worked example
Worked example / 例题
A trapezium has parallel sides 5 cm and 9 cm, and a height of 4 cm. Find its area.
A = ½ × (a + b) × height = ½ × (5 + 9) × 4 = ½ × 14 × 4 = 28 cm².
Working backwards
You can also find a missing length. If a triangle has area 24 cm² and base 8 cm, then ½ × 8 × height = 24, so 4 × height = 24 and height = 6 cm.
Remember / 记住
- Area uses square units (cm², m²).
- Use the perpendicular height, not a slanted edge.
- Do not forget the ½ for a triangle, kite or trapezium.