Properties
The parallel sides of a trapezoid are called the bases of the trapezoid. In the general case, in which the quadrilateral has only one pair of parallel sides, the sides are called the short base and the long base.
Based on its properties, a trapezoid also belongs to the family of quadrilateral.
Formula
The area A of a trapezoid whose bases are b and B and whose height is h is: \(A=\frac{(B +b) × h}{2}\).
Educational notes
The problem with definitions is that students often have a tendency to limit their meaning, rather than understand them from a general perspective.
For example, a quadrilateral with a pair of parallel sides is called a “trapezoid,” but that does not mean that a trapezoid can only have one pair of parallel sides. For this reason, “at least one pair of parallel sides” is specified. As a result, all parallelograms are trapezoids. If the definition were to be understood in the strictest sense, then a quadrilateral with more than one pair of parallel sides would no longer have just one pair and would not be a trapezoid!
That’s quite a paradox!
If the other properties of a trapezoid are considered, including the method of calculating its perimeter and area, it can be noted that these properties also apply to parallelograms.
It should be specified that although a parallelogram has congruent opposite sides, it is not an isosceles trapezoid, however, a rectangle is, since it satisfies the definition of an isosceles trapezoid, which states that an isosceles trapezoid is symmetric about the perpendicular bisector to its bases. An isosceles trapezoid can be inscribed in a circle, which is a property that not all parallelograms have.
When discussing trapezoids in general, we do not focus on particular cases, such as parallelograms, rhombuses, rectangles or squares, which are understood to be special types of trapezoids.
It should be noted that older definitions, such as the one in the Nouveau manuel complet d’architecture by M. Toussaint, published in 1837 (page 32), specify that “[a] trapezoid has only two parallel sides […]”.