Understand the rectangle

A rectangle is a quadrilateral with four right angles. Opposite sides are equal and parallel. The two adjacent side lengths determine its area, perimeter and diagonal.

Properties that make the calculations work

The diagonals are equal and bisect one another. A square is a rectangle whose adjacent sides happen to be equal. Unless it is a square, the diagonals are not perpendicular.

Where the model is useful

Measure a room outline, a page or a screen using a common unit. Inverse calculators recover a missing side from area, perimeter or diagonal when one side is already known.

Measure the right thing

Do not use a sloping distance as a side. A diagonal must exceed the known adjacent side.

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: Rectangle 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.