A trapezoid is a 4 sided quadrilateral that has a pair of opposite parallel sides of different lengths and it can also be classified as an isosceles trapezoid when it has one line of symmetry
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All the names to classify a trapezoid are a trapezoid and a quadrilateral.
i think u can classify it in 2 ways
A trapezoid (or trapezium, outside of North America) is a four-sided figure with two opposite sides that are parallel. Thus a trapezoid is a special type of quadrilateral, which is any four-sided figure. A quadrilateral is itself a special type of polygon, which is any figure with straight sides.
by how long it is
A trapezoid is called a trapezium in the UK (because the UK trapezoid is scalene). In any case, a trapezoid is also a quadrilateral, in that it has four sides.