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How to find the length of diagonal of a rhombus?

Last Updated : 18 Feb, 2024
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Rhombus is also known as a four-sided quadrilateral. It is considered to be a special case of a parallelogram. A rhombus contains parallel opposite sides and equal opposite angles. A rhombus is also known by the name diamond or rhombus diamond. A rhombus contains all the sides of a rhombus as equal in length. Also, the diagonals of a rhombus bisect each other at right angles. 

Properties of a Rhombus

A rhombus contains the following properties: 

  • A rhombus contains all equal sides.
  • Diagonals of a rhombus bisect each other at right angles.
  • The opposite sides of a rhombus are parallel in nature.
  • The sum of two adjacent angles of a rhombus is equal to 180o.
  • There is no inscribing circle within a rhombus.
  • There is no circumscribing circle around a rhombus.
  • The diagonals of a rhombus lead to the formation of four right-angled triangles.
  • These triangles are congruent to each other.
  • Opposite angles of a rhombus are equal.
  • When you connect the midpoint of the sides of a rhombus, a rectangle is formed.
  • When the midpoints of half the diagonal are connected, another rhombus is formed.

Diagonal of a Rhombus

A rhombus has four edges joined by vertices. On connecting the opposite vertices of a rhombus, additional edges are formed, which result in the formation of diagonals of a rhombus. Therefore, a rhombus can have two diagonals each of which intersects at an angle of 90°. 

Properties of diagonal of a rhombus 

The diagonals of a rhombus have the following properties: 

  • The diagonals bisect each other at right angles.
  • The diagonals of a rhombus divide into four congruent right-angled triangles.
  • The diagonals of a rhombus may or may not be equal in length.

Computation of diagonal of rhombus 

The length of the diagonals of the rhombus can be calculated by using the following methods: 

By Pythagoras Theorem 

Let us assume d1 to be the diagonal of the rhombus. 

Since, we know, all adjacent sides in a rhombus subtend an angle of 90 degrees.


In the triangle, BCD we have, 

BC2 + CD2 = BD2

Now, we have, 

In the case of a square rhombus with all sides equal, 

Square Diagonal: a√2

where a is the length of the side of the square

In the case of a rectangle rhombus, we have, 

Rectangle Diagonal: √[l2 + b2]


  • l is the length of the rectangle.
  • b is the breadth of the rectangle.

By using the area of rhombus

Let us consider, O to be the point of intersection of two diagonals, namely d1 and d2.


The area of the rhombus is equivalent to, 

A = 4 × area of ∆AOB

= 4 × (½) × AO × OB sq. units

= 4 × (½) × (½) d1 × (½) d2 sq. units

= 4 × (1/8) d1 × d2 square units

= ½ × d1 × d2

Therefore, Area of a Rhombus = A = ½ × d1 × d2

Area of rhombus using diagonals

Consider a rhombus ABCD, having two diagonals, i.e. AC & BD.

  • Step 1: Compute the length of the line segment AC, by joining the points A and C. Let this be diagonal 1, i.e. d1.

The diagonals of a rhombus are perpendicular to each other subtending right triangles upon intersection with each other at the centre of the rhombus.

  • Step 2: Similarly, compute the length of diagonal 2, i.e. d2 which is the distance between points B and D.
  • Step 3: Multiply both the calculated diagonals, d1, and d2.
  • Step 4: The result is obtained by dividing the product by 2.

The resultant will give the area of a rhombus ABCD.

Sample Questions 

Question 1. One of the sides of a rhombus is equivalent to 5 cm. One of the diagonals of the rhombus is 8 cm, compute the length of the other diagonal.


Let us consider, ABCD to be a rhombus, where AC and BD are the diagonals. 

We have, 

Side of the rhombus is 5 cm  

BD = 8 cm   

Since, we know that the diagonals of rhombus perpendicularly bisect each other.  

∴  BO = 4cm 

By Pythagoras theorem, we have, 

 In right angled △AOB,  

⇒  (AB)2 = (AO)2 + (BO)2            

⇒  (5)2 = (AO)2 + (4)2  

⇒  25 = (AO)2 + 16  

⇒  (AO)2 = 9  

∴  AO = 3cm  

⇒  AC = 2 × 3 = 6 cm  

∴  The length of other diagonal of the rhombus is equivalent to 6 cm.

Question 2. Calculate the area of a rhombus with diagonals equivalent to 6 cm and 8 cm respectively.


We know,

Diagonal 1, d1 = 6 cm

Diagonal 2, d2 = 8 cm

Area of a rhombus, A = (d1 × d2) / 2

Substituting the values, 

= (6 × 8) / 2

= 48 / 2

= 24 cm2

Hence, the area of the rhombus is 24 cm2.

Question 3. A rectangular park has 10m length and breadth is 8m. Compute the diagonal of park. 


We have, 

Length = 100m
Breadth = 8 m

Computing diagonals, we obtain, 

Rectangle Diagonal = √[l2 + b2]

= √[102 + 82 ]

= √[164]

= 12.80 m

Question 4. A square rhombus has a side of 5 cm. Compute the length of diagonal. 


We have, 

Side of square, a = 5 units

Computing diagonals, we obtain, 

Square Diagonal = a√2

= 5√2

= 7.07 cm

Question 5.  The area of rhombus is 315 cm² and its perimeter is 180 cm. Find the altitude of the rhombus.


We have, 

Perimeter of rhombus = 180 cm

Calculating for the side of rhombus, 

Side of rhombus,b = P/4 = 180/4 = 45 cm


Area of rhombus = b × h

Substituting the values, 

 ⇒ 315 = 45 × h

⇒ h = 315/45

⇒ h =7 cm

Therefore, altitude of the rhombus is 7 cm.

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