Rhombus - Properties, Definition, Formulas, Examples - Cuemath

Rhombus

A rhombus is a closed two-dimensional plane figure. It is considered a special parallelogram, and because of its unique properties, it gets an individual identity as a quadrilateral. A rhombus is also called an equilateral quadrilateral since all of its sides are equal in length. The term ‘rhombus’ has been derived from the ancient Greek word ‘rhombos', which actually means something that spins. Let us learn more about the rhombus and its properties in this article.

1.	What is a Rhombus?
2.	Properties of a Rhombus
3.	What does a Rhombus look like?
4.	Rhombus Formulas
5.	FAQs on Rhombus

What is a Rhombus?

A rhombus can be defined as a special parallelogramas it fulfills the requirements of a parallelogram, i.e. a quadrilateral with two pairs of parallel sides. In addition to this, a rhombus has all four sides equal just like a square. That is why it is also known as a tilted square. Look at the image below to understand the relationship of rhombus shape with parallelogram and square.

In the above figure, we can notice that every rhombus we see will also be a parallelogram, but not every parallelogram is a rhombus. A square can be considered as a special case of a rhombus because it has four equal sides. All the angles of a square are right angles, but the angles of a rhombus need not necessarily have to be right angles. And, hence a rhombus with right angles can be considered a square. Hence, we can conclude that:

• All rhombi or rhombuses are parallelograms, but all parallelograms are not rhombuses.
• All rhombi or rhombuses are not squares, but all squares are rhombuses.

A rhombus can have three additional names:

• Diamond
• Lozenge
• Rhomb

Properties of a Rhombus

A rhombus is considered to be one of the special parallelograms as it has all the properties of a parallelogram. A rhombus has its two diagonals as its two lines of symmetry. Axis of symmetry can be considered as a line that divides an object into two equal halves. It creates a mirror-like reflection of both sides of the object. A rhombus is said to have reflection symmetry over both of its diagonals. The general properties of a parallelogram are as follows:

• Opposite angles are congruent or equal.
• The opposite sides are equal and parallel.
• Diagonals bisect each other.
• The sum of any two adjacent or consecutive angles is 180°.

A rhombus, like all geometric shapes, has properties that are unique to it. The table below describes the properties of a rhombus.

Properties of Rhombus	Reference
All sides of a rhombus are congruent (equal).	Here, AB = CD = DA = BC
Diagonals bisect each other at 90° or we can also say that each of the two diagonals in a rhombus is the perpendicular bisector of the other.	Here, diagonals DB and CA bisect each other at 90°
Opposite angles are equal and the opposite sides are parallel.	Here, CD || AB and BC || AD. ∠A = ∠C and ∠D = ∠B
Adjacent anglesadd up to 180°	∠A + ∠B = 180° ∠B + ∠C = 180° ∠C + ∠D = 180° ∠A + ∠D = 180°

One thing we should remember about the diagonal of a rhombus is that in addition to bisecting each other at 90°, the two diagonals bisected will be of the same length. For example: if the length of a diagonal is 10 cm and the other diagonal bisects it, then it is divided into two 5 cm segments. If you know the side of the rhombus and the value of certain angles, then you can determine the length of the diagonal.

What Does a Rhombus Look Like?

A rhombus is a diamond-shaped quadrilateral that has all four sides equal. We can see rhombus-shaped figures in our day-to-day lives. Some of the real-life examples of a rhombus are shown in the below-given figure: a diamond, a kite, an earring, etc.

Rhombus Formulas

The formulae for rhombuses are defined for two attributes:

1. Area of a rhombus, A = 1/2 × d1 × d2, where d1 and d2 are diagonals of a rhombus.
2. The perimeter of a rhombus, P = 4 × a, where a is the side.

Area and Perimeter of a Rhombus

The area of a rhombus can be defined as the amount of space enclosed or encompassed by a rhombus in a two-dimensional plane. It is half of the product of the lengths of the diagonals. So, A = 1/2 × d1 × d2, where d1 and d2 are the lengths of the diagonals.

Just like a square, all four sides of a rhombus are equal, so, the formula for the perimeter of the rhombus is the product of the length of one side by 4. We get P = (4 × a) units, where a is the side of a rhombus.

☛ Important Notes on Rhombus

Here is a list of a few points that should be remembered while studying about rhombus:

• Adjacent angles in a rhombus are supplementary, they sum up to 180°.
• Diagonals bisect each other at right angles.
• All squares are rhombuses, but not all rhombuses are squares.

☛ Related Topics:

Check out these interesting articles to learn more about the rhombus and its related topics.

• Rhombus Area Calculator
• Rhombus Worksheets
• Difference Between Kite and Rhombus

Cuemath is one of the world's leading math learning platforms that offers LIVE 1-to-1 online math classes for grades K-12. Our mission is to transform the way children learn math, to help them excel in school and competitive exams. Our expert tutors conduct 2 or more live classes per week, at a pace that matches the child's learning needs.