Properties of a Trapezium
A trapezium is a quadrilateral with exactly one pair of parallel sides. Those parallel sides are the bases; the other two are the legs. Its area is ½ × (sum of the parallel sides) × height, and its four interior angles add up to 360°.
Key properties of a trapezium
| Property | Detail |
|---|---|
| Sides | 4 (one pair parallel) |
| Parallel sides | The two bases (a and b) |
| Area | ½ × (a + b) × h |
| Perimeter | Sum of all four sides |
| Sum of interior angles | 360° |
| Co-interior angles (on each leg) | Add up to 180° |
Angle properties
Because the two bases are parallel, each leg is a transversal cutting them. The two angles on the same leg (co-interior angles) therefore add up to 180°. All four interior angles together add up to 360°, as in any quadrilateral.
Types of trapezium
An isosceles trapezium has equal legs and equal base angles, and its diagonals are equal in length. A right trapezium has two right angles. A scalene trapezium has all sides and angles different.
Note the naming difference: in British English a 'trapezium' has one pair of parallel sides; in American English the same shape is a 'trapezoid'.
Worked examples
Find the area of a trapezium with parallel sides 8 cm and 12 cm and height 5 cm.
- Area = ½ × (a + b) × h
- = ½ × (8 + 12) × 5
- = ½ × 20 × 5
- = 50 cm².
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Related concepts
Frequently asked questions
Area = ½ × (sum of the two parallel sides) × the perpendicular height, or ½ × (a + b) × h.
A trapezium has exactly one pair of parallel sides.
In British English, a trapezium has one pair of parallel sides; American English calls that shape a trapezoid. They refer to the same figure.