What is a trapezium?
A trapezium is a flat shape with four straight sides and exactly one pair of parallel sides.
The answer
A trapezium has 4 sides, 4 vertices and 1 pair of parallel sides. The one drawn here has 0 lines of symmetry. An isosceles trapezium, with its two sloping sides equal, has 1. The angles inside a trapezium add up to 360°.
Trapezium diagram and properties
| Property | Count |
|---|---|
| Sides | 4 |
| Vertices (corners) | 4 |
| Angles add up to | 360° |
| Right anglesA right-angled trapezium has 2. | 0 |
| Pairs of parallel sides | 1 |
| Lines of symmetryAn isosceles trapezium, with its two sloping sides equal, has 1. | 0 |
Key facts about the trapezium
- The two parallel sides are always different lengths. If they were the same length, the other two sides would be parallel too, and the shape would be a parallelogram.
- The two angles along each sloping side add up to 180°, because they sit between the same pair of parallel lines.
- In the USA this shape is called a trapezoid. In the UK, trapezium is the word used in school and in the 11+.
Where you see it
A bucket seen from the side, a handbag, a lampshade and the cross-section of many roofs are all trapezium shapes.
The common mistake
Calling any four-sided shape with slanted sides a trapezium. Check for the one pair of parallel sides first: a kite has slanted sides but no parallel sides at all.
An 11+ style question
A trapezium has angles of 70°, 110° and 65°. What is the fourth angle?
Answer: 115°
- The four angles of any quadrilateral add up to 360°.
- 70 + 110 + 65 = 245
- 360 − 245 = 115, so the fourth angle is 115°.
Related shapes and skills
More shapes
Questions parents ask
How many sides and vertices does a trapezium have?
A trapezium has 4 straight sides and 4 vertices (corners). Its angles add up to 360°.
How many lines of symmetry does a trapezium have?
A trapezium like the one drawn here has 0 lines of symmetry. An isosceles trapezium, with its two sloping sides equal, has 1.
Is a trapezium the same as a trapezoid?
Yes, in the sense that a UK trapezium is what Americans call a trapezoid: four sides with one pair of parallel sides. UK schools and 11+ papers always say trapezium.
Is a parallelogram a trapezium?
Not in the way primary schools in England teach it. A trapezium has exactly one pair of parallel sides, and a parallelogram has two. Some secondary textbooks use a wider definition, "at least one pair", so it is worth knowing both exist.
Do children need the area of a trapezium formula for the 11+?
The formula is taught in Key Stage 3, not primary school. In the 11+, a trapezium area question can usually be solved by splitting the shape into a rectangle and triangles, which Year 6 children do learn.
Shape questions are quick marks in the 11+
Angles, symmetry, nets and 3D shapes come up in 11+ maths and non-verbal reasoning. The free diagnostic checks maths, English and both kinds of reasoning, and shows what to practise next. No card is required.