Formula sheet
Area of trapezium
(1/2) × sum of two parallel sides × height is given on the exam formula sheet. You must still identify the two parallel sides, use the perpendicular height (not a slanted side), and remember the ½.
What the symbols mean
- a, b The two parallel sides of the trapezium (length unit).
- h Perpendicular height, the straight distance between the two parallel sides (length unit).
Given in the exam, or memorise?
(1/2) × sum of two parallel sides × height is given on the exam formula sheet. You must still identify the two parallel sides, use the perpendicular height (not a slanted side), and remember the ½.
Why it works
Two copies of a trapezium make a parallelogram.
- Take the trapezium and a flipped copy of it.
- Together they form a parallelogram of base (a + b) and height h, area (a + b) × h.
- One trapezium is half of that: ½ × (a + b) × h.
Worked example 1
A trapezium has parallel sides 8 cm and 12 cm and height 5 cm. Find its area.
- Area = ½ × (a + b) × h
- = ½ × (8 + 12) × 5
- = ½ × 20 × 5
- = 10 × 5 = 50
Worked example 2
A trapezium has area 90 cm² and parallel sides 9 cm and 21 cm. Find its height.
- Area = ½ × (a + b) × h
- 90 = ½ × (9 + 21) × h
- 90 = ½ × 30 × h = 15h
- h = 90 ÷ 15 = 6
Where students go wrong
- Using a slanted side as the height instead of the perpendicular distance between the parallel sides.
- Adding all four sides instead of only the two parallel ones.
- Forgetting the ½, which doubles the area.
- Answering in cm instead of cm².
Use it with
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
Which sides are the parallel sides?
They are the two sides that never meet however far you extend them, usually the top and bottom edges drawn horizontally. In a diagram they are often marked with matching arrows.
Only these two go into (a + b); the two slanted sides are not used in the area formula at all.
What counts as the height of a trapezium?
The height is the perpendicular gap between the two parallel sides, measured at a right angle to them, not along a slanted edge. A slanted side is longer than the true height, so using it inflates the area.
Look for the small right-angle mark in the diagram to find the correct h.
Is the trapezium area formula given in SPM?
Yes, ½ × sum of two parallel sides × height is printed on the formula sheet. You are assessed on applying it: picking the two parallel sides, using the perpendicular height, and keeping the ½.
Because it is provided, focus your practice on reading diagrams correctly rather than on recalling the formula.