Trapezoid - math word definition (original) (raw)
A quadrilateral which has at least one pair of parallel sides
(but see definition notes below)
Try this Drag the orange dots on each vertexto reshape the figure. Notice that the sides AB and CD remain parallel.
Attributes
| Base | One of the parallel sides. Every trapezoid has two bases. See Base definitions. |
|---|---|
| Leg | The sides AC and BD above are called the legs of the trapezoid, and are usually not parallel, although they could be (see parallelogram note below). Every trapezoid has two legs. |
| Altitude | The altitude of a trapezoid is the perpendicular distance from one base to the other. (One base may need to be extended). |
| Median | The median of a trapezoid is a line joining the midpoints of the two legs. See Trapezoid median |
| Area | The usual way to calculate the area is the average base length times altitude. See Area of a Trapezoid |
| Perimeter | The distance a round the trapezoid. The sum of its side lengths. See Perimeter of a Trapezoid |
If both legs are the same length, this is called an isosceles trapezoid, and both base angles are the same.
If the legs are parallel, it now has two pairs of parallel sides, and is a parallelogram.
Coordinate Geometry
In coordinate geometry, if you know the coordinates of the four vertices, you can calculate various properties of it, including the altitude and median. For more on this, see Trapezoid definition (Coordinate Geometry)
Definition notes
There is considerable confusion over the definition of 'trapezoid' and 'trapezium' due to differences in the British and US versions. As you can see from the table below, the meanings of the two words are exactly reversed between the US and British interpretations.
| | British | USA | | | -------------- | ----------------------------------------------- | ----------------------------------------------- | | Trapezoid | A quadrilateral with no sides parallel | A quadrilateral with one pair of parallel sides | | Trapezium | A quadrilateral with one pair of parallel sides | A quadrilateral with no sides parallel |
Other polygon topics
General
- Polygon general definition
- Quadrilateral
- Regular polygon
- Irregular polygon
- Convex polygons
- Concave polygons
- Polygon diagonals
- Polygon triangles
- Apothem of a regular polygon
- Polygon center
- Radius of a regular polygon
- Incircle of a regular polygon
- Incenter of a regular polygon
- Circumcircle of a polygon
- Parallelogram inscribed in a quadrilateral
Types of polygon
- Square
- Diagonals of a square
- Rectangle
- Diagonals of a rectangle
- Golden rectangle
- Parallelogram
- Rhombus
- Trapezoid
- Trapezoid median
- Kite
- Inscribed (cyclic) quadrilateral
Area of various polygon types
- Regular polygon area
- Irregular polygon area
- Rhombus area
- Kite area
- Rectangle area
- Area of a square
- Trapezoid area
- Parallelogram area
Perimeter of various polygon types
- Perimeter of a polygon (regular and irregular)
- Perimeter of a triangle
- Perimeter of a rectangle
- Perimeter of a square
- Perimeter of a parallelogram
- Perimeter of a rhombus
- Perimeter of a trapezoid
- Perimeter of a kite
Angles associated with polygons
- Exterior angles of a polygon
- Interior angles of a polygon
- Relationship of interior/exterior angles
- Polygon central angle
Named polygons
- Tetragon, 4 sides
- Pentagon, 5 sides
- Hexagon, 6 sides
- Heptagon, 7 sides
- Octagon, 8 sides
- Nonagon Enneagon, 9 sides
- Decagon, 10 sides
- Undecagon, 11 sides
- Dodecagon, 12 sides
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