Rhombus
A rhombus is a twodimensional plane figure with a closed shape. It is considered a special parallelogram, and because of its unique properties, it gets an individual identity as a quadrilateral. Rhombus is also called an equilateral quadrilateral, since equilateral means that 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.
In this article, let's learn about the rhombus, understand its shape, properties, and the area and the perimeter of a rhombus using solved examples.
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 parallelogram as it fulfills the requirements of a parallelogram, a quadrilateral with two pairs of parallel sides. In addition to this, a rhombus also has four equal sides, but it is still a type of parallelogram with four congruent sides. Hence, a rhombus fits all the properties of a parallelogram. We can notice how the four sides remain the same length and the opposite sides remain parallel.
In the abovegiven figure, we can notice that every rhombus we see will also be a parallelogram, but not every parallelogram we see will be a rhombus. A square can be considered as a special case of a rhombus because it has four equallength 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 mirrorlike reflection of both the side 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  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 angles add 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 in addition to bisecting each other at 90°, the two diagonals bisected will be 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 diagonals. 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 diamondshaped quadrilateral that has all four sides equal. We can see rhombusshaped figures in our daytoday lives. Some of the reallife examples of a rhombus are shown in the belowgiven figure: a diamond, a kite, and an earring, etc.
Rhombus Formulas
The formulae for rhombuses are defined for two features:
 Area of a rhombus, where \(A = \dfrac{{d_1 d_2 }}{2}\), where d1 and d2 are diagonals of a rhombus
 The perimeter of a rhombus, where P = 4×a, 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 twodimensional plane. product of the lengths of the diagonals.
\(A = \dfrac{{d_1 d_2 }}{2}\) Sq. units, Where \(d_1\) and \(d_2\) are the lengths of the diagonals.
Just like a square, all four sides of a rhombus are equal, so, the formula for the perimeter is the product of the length of one side with 4
Perimeter P = 4 × side units, Here 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 and at equal lengths
 All squares are rhombuses, but not all rhombuses are squares
☛ Related Topics:
Solved Examples on Rhombus

Example 1: David has drawn a rhombus where the lengths of the two diagonal lengths \(d_1\) and \(d_2\) of a rhombus are 5 units and 10 units, respectively. He asks his sister Linda to help him find the area. Can you help Linda find the answer?
Solution:
Given:
Diagonal d1 = 5 units, and d2 = 10 units
A = (d1 × d2)/2
A = (5×10)/2
A = 25 sq. units
Answer: The area of the rhombus = 25 sq. units

Example 2: Elsa was given the area of a rhombus and the length of one diagonal. The area given was 100 square units and the length of a diagonal was 20 units. Can you help Elsa find the length of the other diagonal?
Solution:
Given:
Area = 100 Sq. units, and diagonal d1 = 20 units
= (d1 × d2)/2
100 = (20 ×d2)/ 2
d2 = 10 units
Answer: The length of the other diagonal d2 = 10 units

Example 3: Sam and Victor were playing a game of hopscotch and they spotted a rhombusshaped tile at the playground. Somebody had inscribed 15 units along the length of the tile. Can you help Sam and Victor find the perimeter of the tile?
Solution:
Given:
Length of the tile = 15 units.
Since all sides of a rhombus are equal, all four sides are equal to 15 units.
Perimeter = 4 × side = 4 × 15 = 60 units
Answer: The perimeter of the tile = 60 units.
FAQs on Rhombus
What is Rhombus in Geometry?
A rhombus is a 2D shape with four sides hence termed as a quadrilateral. It has two diagonals that bisect each other at right angles. It also has opposite sides parallel and the sum of all the four interior angles is 360 degrees.
Are All Squares Rhombuses?
Yes, all squares are rhombuses. A square can be considered as a special case of a rhombus because it has four equallength 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.
What Shape Is a Rhombus?
A rhombus is a diamondshaped quadrilateral. If you look at a pack of cards and pull out the 13 diamond cards, you will find that the diamond geometric shape is that of a rhombus.
Is a Rhombus a Regular Polygon?
No, a rhombus is not a regular polygon. A regular polygon must be equiangular (all of its angles are the same measure) and congruent or, equilateral (all of its sides are the same length). But a rhombus is only equilateral: all of its sides are of the same length and only the opposite angles are equal. A rhombus can never be considered a regular polygon as it is only an equilateral polygon and not an equiangular polygon.
What Is the Area of a Rhombus?
The area of a rhombus is calculated by dividing the product of the diagonals by 2. Mathematically, this can be defined as: \(A = \frac{{d_1 d_2 }}{2}\), where d1 and d2 are the diagonals of a rhombus
What Are the Four Properties of a Rhombus?
A rhombus is a quadrilateral that has the following four properties: Opposite angles are always equal, all sides are equal and, opposite sides are parallel to each other, diagonals bisect each other perpendicularly and at equal lengths, the sum of any two adjacent angles will always be supplementary 180°
What is the Difference Between Rhombus and a Square?
The main difference between a rhombus and a square is that the angles of a rhombus are not equal to 90° whereas all the angles of a square are equal to 90°. It is often said that a square is a rhombus, but a rhombus isn’t always a square.
What Is the Difference Between a Parallelogram and a Rhombus?
The difference between a parallelogram and a rhombus is that in a rhombus all four sides are equal in measurement, whereas a parallelogram has opposite sides equal.
What are the Basic Rhombus Formulas?
Few basic rhombus formulas are listed below:
 Area of the rhombus = 1/2 × d1 × d2
 Perimeter of a rhombus = 4 × side
What is the Sum of the Interior Angles in a Rhombus?
The sum of the interior angles in a rhombus is 360°.
Are All Angles of a Rhombus 90°?
No, the angles of a rhombus need not necessarily have to be right angles, although they are all equal.