Understand the parallelogram

A parallelogram is a quadrilateral with both pairs of opposite sides parallel. Opposite sides and opposite angles are equal. Rectangles, rhombi and squares are special cases.

Properties that make the calculations work

Adjacent angles add to 180 degrees. The diagonals bisect one another but are generally neither equal nor perpendicular. Area is base times the perpendicular distance between the parallel base lines.

Where the model is useful

Use base and height for area only. To find perimeter and diagonals, supply the two side lengths and their included angle. Diagonal lengths with their crossing angle can also determine area.

Measure the right thing

A sloping side is not generally the height. Base and height alone do not determine perimeter.

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: Parallelogram 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.