trapezoidal

Trapezoidal is an adjective used to describe things shaped like a trapezoid, a four‑sided polygon with a pair of parallel sides. In geometry, the parallel sides are called the bases and the nonparallel sides are the legs. The term is also used for solids and cross‑sections that carry a trapezoidal profile, as well as in phrases referring to methods or shapes named after the trapezoid.

Two‑dimensional properties: The area of a trapezoid equals the average of the base lengths times the height: A = (b1 + b2)/2 · h, where b1 and b2 are the lengths of the bases and h is the perpendicular distance between them. If the legs are equal and the base angles are equal, the trapezoid is isosceles; in that case, the diagonals are equal in length. If both pairs of opposite sides are parallel, the figure is a parallelogram and is typically not described as trapezoidal in strict usage.

Three‑dimensional: A trapezoidal prism is formed by extruding a trapezoid along a perpendicular axis, and its volume is the area of the trapezoidal base times the extrusion height. A trapezoidal pyramid has a trapezoidal base with triangular side faces.

Other uses: The term also appears in calculus as the trapezoidal rule, a method for approximating definite integrals that partitions the area under a curve into trapezoids. In probability and statistics, a trapezoidal distribution describes a continuous shape whose probability density function forms a trapezoid, defined by its support and plateaus. The adjective is common in engineering, design, and descriptive geometry to indicate a trapezoid‑like profile.