Trapezoid

In geometry, A trapezoid (in North America) or trapezium (in Britain and elsewhere) is a quadrilateral, which is defined as a shape with four sides. This shape has two parallel sides which are called the bases of the trapezoid, and another two sides called its legs. In North America, the term "trapezium" is used for what is elsewhere called an irregular quadrilateral, which has no parallel sides.

Special cases

Some trapezoids are special cases where they have at least one noteworthy feature:

• Isosceles trapezoids: These have legs that are of the same length, and because of that, this trapezoid has a pair of angles of the same wideness (congruent).
• Parallelogramsː This is a trapezoid where two pairs of its sides are parallel to each other. As a result, there are two pairs of vertices in a parallelogram that are congruent.
• Tangential trapezoidsː These are trapezoids whose sides can be tangent to a circle placed inside of them, to which the circle is called an incircle.

Calculating area

To calculate the area of a trapezoid, you must add the two parallel sides together, divide that by 2, then times that by its height.

[math]\displaystyle{ A = \frac{a + b}{2} \cdot h }[/math]

Trapezoid Media

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  Trapezium and Trapezoid, Hutton’s mistake in 1795

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  Set of geometric shapes

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  Set of geometric shapes

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  a quadrilateral having only two sides parallel

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  a quadrilateral having only two sides parallel

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  a quadrilateral with no parallel sides

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  Trapezoid special cases. The orange figures also qualify as parallelograms.

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  general trapezoid/trapezium:parallel sides: a,\, b with a

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  trapezoid/trapezium with opposing triangles S,\,T formed by the diagonals

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  A trapezium (or trapezoid).

Other websites

• "Trapezoid" on MathWorld
• Trapezoid definition   Area of a trapezoid   Median of a trapezoid With interactive animations
• Trapezoid (North America) at elsy.at: Animated course (construction, circumference, area)