Sheet № 99 · Foundation + Higher · AQA · Edexcel · OCR
Area of a Trapezium –
The trapezium is one of the most commonly tested shapes at GCSE, and the good news is its area formula is given on every exam board's formula sheet. You still need to know how to use it correctly — identifying the parallel sides, choosing the perpendicular height, and applying the formula within compound shapes.
§Key definitions
Question:
A trapezium has parallel sides of 6 cm and 10 cm and a perpendicular height of 4 cm. Find its area.
Q1 (Foundation):
A trapezium has parallel sides of 9 cm and 15 cm and a perpendicular height of 6 cm. Find its area.
Q2 (Foundation):
A trapezium has parallel sides of 4.5 cm and 7.5 cm and a perpendicular height of 8 cm. Find its area.
Q3 (Higher):
A trapezium has an area of 84 cm². One parallel side is 10 cm and the perpendicular height is 7 cm. Find the length of the other parallel side.
§Formulas to memorise
A = ½(a + b) × h, where a and b are the parallel sides and h is the perpendicular height
For a compound shape containing a trapezium, find the trapezium area separately and add or subtract as needed
Substitute into the formula A = ½(a + b) × h and calculate.
A = ½(a + b) × h
A = ½(6 + 10) × 4
A = ½ × 16 × 4
A = 8 × 4
A = 32
h = 60 ÷ 10
h = 6
Worked example
A trapezium has parallel sides of 6 cm and 10 cm and a perpendicular height of 4 cm. Find its area.
Working: A = ½(a + b) × h A = ½(6 + 10) × 4 A = ½ × 16 × 4 A = 8 × 4 A = 32
⚠ Common mistakes
- ✗Using a slant side instead of the perpendicular height. The height must be at right angles to both parallel sides, not along a sloping edge. Look for the right-angle symbol on the diagram.
- ✗Mixing up the parallel and non-parallel sides. Only the two parallel sides go into the formula — the other two sides are not used for the area calculation.
- ✗Forgetting to halve. The formula includes ½. Missing it will double your answer. Write the formula first to avoid this.
- ✗Not including units. Area is always measured in square units — cm², m², etc. Always state the correct unit in your final answer.
✦ Exam tips
- →The formula is on the formula sheet, but write it in your working — this earns a method mark even if you make an arithmetic slip.
- →If a trapezium appears inside a compound shape, deal with it separately and then combine areas at the end.
- →When the height is not labelled directly, look for a right-angle symbol or a dashed line — this indicates the perpendicular height.