---
title: "Rhombus: Four Equal Sides and Diagonals That Cross at Right Angles"
url: https://www.learningloftinstitute.com/glossary/rhombus
source: Learning Loft Institute
language: en
updated: 2026-08-21
section: "Glossary › Rhombus: Four Equal Sides and Diagonals That Cross at Right Angles"
---
# Rhombus: Four Equal Sides and Diagonals That Cross at Right Angles
> **Answer.** A rhombus is a quadrilateral with four sides of equal length. Its opposite sides are parallel, its opposite angles are equal, and its diagonals bisect each other at right angles. Every square is a rhombus with right angles, and every rhombus is a parallelogram with all four sides the same.
## Key facts
| | |
| --- | --- |
| Definition | A rhombus is a quadrilateral with four sides of equal length whose opposite sides are parallel and whose diagonals cross at right angles. |
| Where students meet it | Grade 5 mathematics, when quadrilaterals are sorted by side and angle properties, and again at GCSE in vector proofs about parallelograms. |
| Also known as | Diamond |
## What has to be true before it counts
Only one condition is imposed: all four sides the same length. Everything else on the list below is a consequence of that, not an extra requirement, which is why a rhombus can be drawn leaning heavily to one side and still be a rhombus.
Note what is absent. Nothing here says the angles are 90 degrees, and nothing says the diagonals are the same length. In a typical rhombus one diagonal is noticeably longer than the other.
Diagrams mark a rhombus with a single dash on all four sides. If instead one pair carries a single dash and the other pair a double dash, only opposite sides have been declared equal and the shape is a parallelogram, where the diagonals cannot be assumed perpendicular.
- Four sides of equal length
- Opposite sides parallel, so opposite angles are equal and adjacent angles add to 180 degrees
- Diagonals bisect each other at right angles
- Each diagonal bisects the two corner angles it passes through
- Two lines of symmetry, both running along the diagonals
- Rotational symmetry of order 2
## Is a square a rhombus?
Yes, and the answer is not a technicality. A square has four equal sides, which is the whole definition, so every square is a rhombus. What a square adds is four right angles, and that extra condition also forces its diagonals to be equal.
The reverse is false. A rhombus is only a square when its angles happen to be 90 degrees, so a question that gives you a rhombus has not given you right angles and you cannot use Pythagoras on the sides as though it had.
## Two routes to the area, and when each is quicker
Because a rhombus is a parallelogram, base times perpendicular height works. If a diagram marks a base and a height at right angles to it, that is the shorter route.
When the diagonals are the ones labelled, use half their product instead. The right-angled crossing splits the rhombus into four congruent right-angled triangles, and adding those four areas gives exactly half of one diagonal multiplied by the other.
## Questions
### Is a rhombus the same as a diamond?
Diamond is the everyday word for the shape and rhombus is the mathematical one. They describe the same figure, but a diamond drawn on a playing card usually sits balanced on a point, whereas a rhombus can lean any way it likes. Use rhombus in written work; examiners mark the mathematical term.
### What is the difference between a rhombus and a parallelogram?
A parallelogram needs opposite sides equal and parallel. A rhombus needs all four sides equal, which is a stricter demand, so every rhombus is a parallelogram but most parallelograms are not rhombuses. The visible difference shows in the diagonals: they cross at right angles in a rhombus and at some other angle in a general parallelogram.
### Are the diagonals of a rhombus equal?
Not usually. They cross at right angles and cut each other exactly in half, but their lengths differ unless the rhombus is a square. Equal diagonals are the property of rectangles and squares, and mixing the two facts up is the commonest error on this shape.
### How do you find the side of a rhombus from its diagonals?
Halve both diagonals, then treat them as the two shorter sides of a right-angled triangle. Diagonals of 10 cm and 24 cm give legs of 5 cm and 12 cm, and Pythagoras returns a side of 13 cm. The right angle at the crossing point is what makes this work.
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