## Introduction

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 them.

### What is a Square?

A 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.

The 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 x 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 the 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.

The below table shows some points on similarities between rhombus and square.

### Is a Square a Rhombus?

Square is a rhombus because like a 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 Examples

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 = \[\frac{1}{2} (d_{1} \times d_{2})\]

= \[\frac{1}{2}\](12 x 8)

=\[\frac{1}{2}\]96

= 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 cm

### Interesting Facts

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

Sometimes a rhombus is called a 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 was initially recorded in the 1560s

### Quiz Time

1. 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

2. 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

### Conclusion

In conclusion, the differences between square and rhombus are as follows:

In a square, all interior angles measure 90 degrees (i.e, right angle). In a rhombus, the opposite angles are of the same value.

The lengths of diagonals of a square are of the same measure. The lengths of diagonals of a rhombus are of different measures.

Square has four lines of symmetry but the rhombus has two lines of symmetry.

A square can be drawn within a circle whereas a rhombus cannot be engraved in a circle.

The sides of the square are vertical to each other. But in the rhombus, the sides are not vertical to each other.

## FAQs on Difference Between Square and Rhombuss for JEE Main 2024

**1. 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 and ∠B = ∠D (opposite angles of parallelogram are equal)

**2. What are the properties of a parallelogram?**

**The four common properties of a 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 themselves into two congruent triangles.

The diagonals of a parallelogram bisect each other.

**3. 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 =\[\frac{(D_{1} \times D_{2})}{2}\]

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 the side of a square

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

**4. Can a square be a rhombus?**

Yes, a square appears under the class of a rhombus since it fulfils the properties of a rhombus in which all the sides are equal in length, the diagonals are perpendicular to each other, and the opposite angles are of equal measure.

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