Trapezoid

A trapezoid is a geometric shape with four sides, at least two of which are parallel to each other. The two parallel sides are called bases, while the other two are called legs. The perpendicular distance between the two bases is called the height.

The trapezoid is among the most commonly taught shapes in basic geometry, as it connects the parallelogram and general quadrilaterals. If both pairs of opposite sides are parallel, the shape becomes a parallelogram, which may be considered a special case of a trapezoid.

Basic properties

The sum of the interior angles of a trapezoid is 360 degrees. The two angles on the same leg (between the two bases) are supplementary, summing to 180 degrees, because they lie between two parallel lines cut by a transversal.

Calculating area

The area of a trapezoid is found by adding the two bases and multiplying by the height, then dividing by two: A = ((a + b) ÷ 2) × h, where a and b are the two bases and h is the perpendicular distance between them. This formula reflects the fact that the area equals that of a rectangle whose width is the average of the two bases.

Types

An isosceles trapezoid has two legs of equal length, and the angles at each base are equal to each other. The angle bisector can divide it into two congruent parts. A right trapezoid has at least one angle of 90 degrees. The line segment connecting the midpoints of the two legs is called the midsegment, and its length is the average of the two bases.