what is a trapezoid?

Answer 1

A trapezoid (in North America) or trapezium (in Britain and elsewhere) is a quadrilateral two of whose sides are parallel to each other. Some authors define it as a quadrilateral having exactly one pair of parallel sides, so as to exclude parallelograms.

The exactly opposite concept, a quadrilateral that has no parallel sides, is referred to as a trapezium in North America, and as a trapezoid in Britain and elsewhere. To avoid confusion, this article uses the North American wording. It also admits parallelograms as special cases of trapezoids (however, in this case, it is assumed that one pair of parallel sides is distinguished, and is the one referred to as "the pair of parallel sides").

In an isosceles trapezoid, the base angles are congruent, and so are the pair of non-parallel opposite sides.If the other pair of opposite sides is also parallel, then the trapezoid is also a parallelogram. Otherwise, the other two opposite sides may be extended until they meet at a point, forming a triangle that the trapezoid lies inside.

A quadrilateral is a trapezoid if and only if it contains two adjacent angles that are supplementary, that is, they add up to one straight angle of 180 degrees (π radians). Another necessary and sufficient condition is that the diagonals cut each other in mutually the same ratio; this ratio is the same as that between the lengths of the parallel sides.

The midsegment of a trapezoid is the segment that joins the midpoints of the other pair of opposite sides. It is parallel to the two parallel sides, and its length is the arithmetic mean of the lengths of those sides.

The area of a trapezoid can be computed as the length of the midsegment, multiplied by the distance along a perpendicular line between the parallel sides. This yields as a special case the well-known formula for the area of a triangle, by considering a triangle as a degenerate trapezoid in which one of the parallel sides has shrunk to a point.

Answer 2

A trapezoid (in North America) or trapezium (in Britain and elsewhere) is a quadrilateral two of whose sides are parallel to each other. Some authors define it as a quadrilateral having exactly one pair of parallel sides, so as to exclude parallelograms.