A rhombus is a quadrilateral with four sides of equal length. It is a special parallelogram, so its opposite sides are parallel and its opposite angles are equal. Its diagonals cross at right angles and cut each other in half, and its area is half the product of the diagonals.
The diagonals cross at 90° and halve each other, making four right triangles with legs 4 and 3 and hypotenuse 5. Area = 8 × 62 = 24.
Formal definition and notation
A rhombus is a quadrilateral ABCD with AB = BC = CD = DA. Every rhombus is a parallelogram; in addition its diagonals AC and BD are perpendicular, each diagonal bisects the angles at its ends, and its area is A = d1d22. A rhombus with a right angle is a square.
Both have four equal sides. A square also has four right angles, so every square is a rhombus, but most rhombuses are not squares.
Rhombusvs.Kite
A kite has two pairs of equal sides that are next to each other, like 5, 5, 8, 8. A rhombus has all four sides equal.
Quick check: 3 questions
Question 1 of 3
A rhombus has diagonals of 9 cm and 4 cm. What is its area?
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Answer: D.9 × 42 = 18. Choice A forgets to halve, B adds the diagonals, and C doubles their sum.
Question 2 of 3
Which is true for every rhombus?
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Answer: A. The diagonals of every rhombus cross at right angles. Right angles and equal diagonals happen only in a square, and a rhombus has two pairs of parallel sides, not one.
Question 3 of 3
One angle of a rhombus measures 50°. What is the angle next to it?
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Answer: B. Neighboring angles add to 180°: 180 − 50 = 130. A is the opposite angle, C uses 90 instead of 180, and D subtracts from 360.
Rhombus: frequently asked questions
Is a square a rhombus?
Yes. A rhombus only needs four equal sides, and a square has four equal sides, so every square is a rhombus. The square is the special rhombus whose angles are all 90 degrees. The reverse is not true: a rhombus with angles of 70 and 110 degrees has equal sides but is not a square.
Is a rhombus a parallelogram?
Yes. A quadrilateral with four equal sides always has its opposite sides parallel, so every rhombus is a parallelogram. It has all the parallelogram properties (equal opposite angles, diagonals that bisect each other) plus extra ones: equal sides and diagonals that meet at right angles.
Is a diamond shape a rhombus?
Usually, yes. The diamond on playing cards or road signs is drawn as a rhombus standing on one corner. “Diamond” is an everyday word, not a math term, so in a math class call it a rhombus. Turning a shape does not change its name: a square tipped onto a corner is still a square.
QuadrilateralA quadrilateral is a polygon with four straight sides, four vertices and four angles. Its four interior angles always add to 360 degrees. Squares, rectangles, rhombuses, parallelograms, trapezoids and kites are special quadrilaterals, each named for extra properties of its sides or angles.Geometry · Grade 2, Grade 3, Grade 5ParallelogramA parallelogram is a four-sided shape whose opposite sides are parallel. Its opposite sides are also equal in length, its opposite angles are equal, and its diagonals cut each other in half. Rectangles, rhombuses and squares are special parallelograms. Its area is base times height: A = bh.Geometry · Grade 3, Grade 5, Grade 6AdditionAddition is the operation that puts amounts together to find the total. The numbers you add are called addends, the answer is the sum, and the sign is the plus sign, +. For example, 7 + 5 = 12. On a number line, adding a positive number means moving to the right.Operations · Kindergarten, Grade 1, Grade 2Right AngleA right angle is an angle that measures exactly 90 degrees, a quarter of a full turn. It looks like the corner of a square or a sheet of paper, and it is marked with a small square at the vertex. Two lines that meet at a right angle are perpendicular.Geometry · Grade 2, Grade 3, Grade 4SquareA square is a quadrilateral with four equal sides and four right angles. It is a special rectangle and a special rhombus at the same time. For a square with side s, the perimeter is 4s, the area is s2, and each diagonal is s√2.Geometry · Kindergarten, Grade 2, Grade 3LengthLength is how long something is: the distance from one end of an object to the other. You measure it by counting equal units laid end to end with no gaps or overlaps, such as inches, feet, centimeters or meters. A new pencil is about 7 inches long.Measurement · Grade 1, Grade 2, Grade 3SideA side is one of the straight line segments that form the outline of a polygon. Two sides meet at each corner, or vertex. A triangle has 3 sides and a square has 4, and adding the lengths of all the sides gives the perimeter.Geometry · Kindergarten, Grade 1, Grade 2HeightHeight is how tall something is: the distance from its bottom to its top, measured straight up and down. In geometry, the height of a shape is the perpendicular distance from a base to the opposite vertex or side, so it always meets the base at a right angle. Area and volume formulas use it.Measurement · Grade 2, Grade 5, Grade 6InchAn inch is a US customary unit of length equal to one twelfth of a foot, about the width of an adult thumb. Its abbreviation is in. Rulers split each inch into halves, quarters, eighths and sixteenths. One inch is exactly 2.54 centimeters, and 12 inches make 1 foot.Measurement · Grade 2, Grade 3, Grade 4PerimeterPerimeter is the total distance around a two-dimensional shape. To find it, add the lengths of all the sides. A rectangle with sides 5 and 3 has perimeter 5 + 3 + 5 + 3 = 16. Perimeter is a length, so it uses length units such as inches or meters, never square units.Geometry · Grade 3, Grade 4, Grade 5CentimeterA centimeter is a metric unit of length equal to one hundredth of a meter, about the width of a fingernail. Its symbol is cm. There are 100 centimeters in 1 meter and 10 millimeters in 1 centimeter, and 1 inch equals 2.54 centimeters.Measurement · Grade 3, Grade 4, Grade 5Right TriangleA right triangle is a triangle with one right angle, an angle of exactly 90 degrees. The two sides that form the right angle are the legs, and the longest side, across from the right angle, is the hypotenuse. Its sides follow the Pythagorean theorem: a2 + b2 = c2.Geometry · Grade 4, Grade 6, Grade 8Pythagorean TheoremThe Pythagorean theorem says that in a right triangle, a2 + b2 = c2. The legs are a and b, the two sides that form the right angle. The hypotenuse, c, is the longest side across from the right angle. Legs of 3 and 4 give 9 + 16 = 25, so the hypotenuse is 5.Geometry · Grade 8, Algebra 1DegreeA degree is the standard unit for measuring an angle, written with the symbol °. One degree is 1360 of a full turn, so a full turn is 360°, a straight angle is 180° and a right angle is 90°. An angle that turns through 25 one-degree angles measures 25°.Geometry · Grade 4, Grade 5, Grade 7Perpendicular LinesPerpendicular lines are lines that intersect to form right angles: their intersection makes a 90-degree angle. The symbol ⊥ means is perpendicular to. On a coordinate plane, two perpendicular lines that are not vertical have slopes that multiply to −1, such as 2 and −12.Geometry · Grade 4, Grade 5, Grade 6AreaArea is the amount of surface a flat shape covers, measured in square units. It counts how many unit squares fit inside the shape, which is why the units are squared. A rectangle’s area is length times width, so a 5 by 3 rectangle has area 15 square units.Geometry · Grade 3, Grade 4, Grade 5TrapezoidA trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are the bases, and the other two sides are the legs. Its area is the average of the bases times the height: A = b1 + b22 × h. In British English it is called a trapezium.Geometry · Grade 3, Grade 5, Grade 6