Understand the rhombus

A rhombus is a quadrilateral with four equal sides. Its opposite sides are parallel, making it a special parallelogram. A square is a rhombus with right angles.

Properties that make the calculations work

Its diagonals bisect each other at right angles and bisect opposite interior angles. The area can be obtained from half the product of the diagonals or from side squared times the sine of an interior angle.

Where the model is useful

Use diagonal measurements for a diamond-shaped drawing and side with perpendicular height for a tilted layout. The side-and-height tool reports the acute interior angle; the supplementary angle gives the same area.

Measure the right thing

Perpendicular height is at most a side length. Diagonals need not have equal lengths.

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.

Continue learning

Wolfram MathWorld: Rhombus 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.