What Are Trapezoids?

Trapezoids have one pair of parallel sides

Trapezoids are quadrilaterals with just one requirement: they must have at least one pair of parallel sides. The other two sides can do whatever they want: there are no requirements for any side lengths or angles.

All the blue shapes in the image below are trapezoids. The red shape is not—it's just an arbitrary, unnamed quadrilateral.

Area:

To find the area of a trapezoid, find the average length of the two parallel sides, then multiply by the height according to this formula:

$$\text{area} = \frac{\text{base 1}+\text{base 2}}{2}\times\text{height}$$

Bases on trapezoids refer to the two parallel sides, and a trapezoid's height will be equal to the distance between the two parallel sides. You can think of the height as the length of an altitude from one of the two parallel sides to the other.

Relationship to other quadrilaterals:

Isosceles trapezoids (shape ABCD above) have non-parallel sides of the same length, and the angles connecting them to each parallel side are congruent.

Parallelograms are trapezoids with two sets of parallel sides.

Rectangles (shape IJKL above) are trapezoids with two sets of parallel lines and only right angles.