Understand the trapezoid

A trapezoid here means a quadrilateral with at least one pair of parallel sides. These parallel sides are called bases. The non-parallel sides are called legs when there is just one parallel pair. Some textbooks use the exclusive “exactly one pair” definition instead.

Properties that make the calculations work

Its height is the perpendicular separation of the bases. The midline joins the midpoints of the legs and has length (a+b)/2. Multiplying this midline by the height gives the area.

Where the model is useful

Use bases and height for general area, or enter all four sides when the bases differ. The isosceles tool assumes equal legs with the bases centred; it also permits the rectangular limiting case.

Measure the right thing

Equal bases with arbitrary legs do not uniquely determine a height. The four-side tool rejects that ambiguous case.

Sketch the figure and mark every known measurement before choosing a calculator. A length measured along an edge is not automatically a perpendicular height. If a formula needs a radius, check that the value has not been measured across a full diameter. Write the unit beside each known quantity before entering it.

Scale and units

Multiplying every length by k multiplies any area by k². This is a useful check: doubling all dimensions cannot merely double an area. Inputs expressed in centimetres produce cm² for area; the unit selector relabels rather than converts entered numbers.

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Wolfram MathWorld: Trapezoid provides reference reading. Our summaries and examples are written for this portal and are not a specialist-reviewed textbook. Try a worked example or suggest a correction.