Difference Between Square and Rhombus

Rhombus and Square Differences

In Geometry, you must have learned about different figures with varied shapes and sizes. Squares and Rhombus are among them which you must have studied in your primary classes. Both square and rhombus have some similarities and also have some differences in their diagonals, length, shapes, and angles. They have some similar properties because they fall under the category of a parallelogram. Here, we will study the difference between square and rhombus as well as similarities between rhombus and square.


What is Square?

Square is a plane figure or a quadrilateral with four equal sides and angles. All the four angles of the square are at right angles. The two opposite sides of a square are always of equal length.

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Properties of a Square

  • The four interior angles of a square are equal to 90°.

  • Four sides of a square are congruent and equal to each other.

  • Opposite sides of a square are equal and parallel to each other.

  • The two diagonals of a square are equal and bisect each other at 90°.

  • The area of a square is equal to side× side.

  • The two equal diagonals of a square make two similar isosceles triangles.


What is a Rhombus?

Rhombus is also known as diamond or rhombus diamond is a parallelogram and a four- sided quadrilateral. In Rhombus, opposite angles and sides are equal in length and parallel. The diagonals of a square bisect each other at 90°. Rhombi or Rhombuses is a plural form of a rhombus.

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Properties of a Rhombus

  • Sides of a rhombus are equal

  • Opposite sides of a rhombus are parallel.

  • Diagonals bisect each other at 90° in rhombus

  • No circumscribing and inscribing circles can be made around rhombus.

  • A diagonal of a rhombus bisects its angles.

  • Two adjacent angles of a rhombus are equal to 180°.


Rhombus and Square Differences and Similarities

The Below Table Shows Some Points on Rhombus and Square Differences.

Square

Rhombus

A square is a four - sided figure or parallelogram with 4 right angles meet at the vertex

A rhombus is also a parallelogram whose opposite angles are equal in length.

The diagonals of a square of equal in size

The diagonals of a rhombus are unequal in size

The sides of a rhombus are perpendicular to one another because all four angles of a square are equal to 90°

The sides of a rhombus are not perpendicular to one another because opposite angles of a rhombus are equal in length.

 

The Below Table Shows Some Points on Similarities Between Rhombus and Square.

Square

Rhombus

A square is considered as a parallelogram

A rhombus is also considered as a parallelogram

The square is a four- sided figure whose all the sides are equal in length

All four sides of a rhombus are also equal in length

The opposite sides of a square are equal to each other.

The opposite sides of a rhombus are also equal to each other.

The two diagonals of a square are perpendicular to each other

Rhombus is a parallelogram whose diagonals are perpendicular bisectors of each other.

 

Is a Square a Rhombus?             

Square is a rhombus because as rhombus all the sides of a square are equal in length. Even, the diagonals of both square and rhombus are perpendicular to each other and bisect the opposite angles. Therefore, we can say the square is a rhombus.

The table drawn above which shows similarities between rhombus and square proves the sentence "Is a square a rhombus"?


Solved Example

1. Calculate the area of a rhombus having diagonals equal to 12 cm and 8 cm.

Solution- Given that,

Diagonal 1 or d₁ =12 cm

Diagonal 2 or d₂ = 8 cm

Area of a rhombus = (d₁ x d₂)

= (12 x 8)/ 2

=96 /2

= 43 cm²


2. Let all the area of the square equal to 8 cm. Find its area, perimeter and length of diagonal.

Solution -Side of a square =8 cm

Area of a square = s²= 8² = 64 cm²

Perimeter of a square = 4 x a= 4 x 8 cm=32 cm

Length of the diagonal of a square = s√2 = 1.414 x 8 =11.312


Facts

  • The word rhombus is derived from the Greek word rhombus, which means ‘Spinning top’.

  • Sometimes rhombus are called as diamond, but not all rhombi are diamond in shape

  • The sum of the four internal angles of a square is 360°.

  • Square which means ‘honest’ or fair is initially recorded in  the 1560s


Quiz Time

Which of the following statements is true about rhombus?

a. All the sides of a rhombus are congruent

b. The diagonals of a rhombus are congruent

c. Rhombus has 4 right angles

d. All of the above


Which of the following statements are true about the square?

a. The diagonals of a square are congruent

b. The sides of a square are congruent

c. The square has four right angles

d. The diagonals of a square are perpendicular

FAQ (Frequently Asked Questions)

What is a parallelogram?

A parallelogram is a special type of quadrilateral whose opposite sides are parallel to each other. 

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In the above figure of Parallelogram, where AD // BC and AB // CD.

AD // BC and AB // CD.

AB = CD and AD = BC (opposite sides of a  parallelogram are equal)

 ∠A = ∠C & ∠B = ∠D (opposite angles  of parallelogram are equal


Properties of a Parallelogram.

The four common properties of parallelogram are:-

  •  The opposite sides of a parallelogram are equal.

  • The opposite angles of a parallelogram are always equal.

  • The two diagonals of a parallelogram divide itself into two congruent triangle

  • The diagonals of a parallelogram bisect each other.


The Most Common Three Types of a Parallelogram Are:-

1. Rhombus

2. Square

3. Rectangle

What are the Important Formulas of Both Rhombus and Square?

Some important formulas of a rhombus which are commonly used are:

Area of a rhombus using diagonals =( D₁ x D₂ ) / 2

D₁= Length of diagonal 1

D₂= Length of diagonal 2

Area of a rhombus using base and height= Base x Height

Area of rhombus using Trigonometry = b₂ x Sin (a), where a is equal to the measurement of any interior angle.

The Perimeter of a rhombus = 4 x a, where a is equal to the side of a rhombus

Some important formulas of a square which are commonly are:-

Area of a square = a², where a is equal to side of a square

The Perimeter of a square = 4a, where a is equal to the side of a square

What is the Difference Between a Square and a Rhombus?

Although square and rhombus are quadrilateral and a parallelogram and have many similarities between them. But with these similarities, there are also some differences between them.

Some most important differences between a square and rhombus are :

  • Square has 4 right angles whereas rhombus does not have any right angle

  • The sides of a square are perpendicular to each other whereas the sides of a rhombus are not perpendicular to each other.

  • All the angles of a square are equal whereas only the opposite angles of a square are equal.

  • The two diagonals of a square are always equal in length while the two diagonals of a rhombus are unequal