Difference Between Square and Rhombus
The main difference between a square and a rhombus is that all the angles of a square are equal to 90°, whereas, the angles of a rhombus are not equal to 90°. It is often said that a square is a rhombus, but a rhombus isn’t always a square because a square fulfills all the properties of a rhombus. When a rhombus satisfies all the properties of a square, it becomes a square. Let us learn more about the difference between square and rhombus.
| 1. | Difference Between Square and Rhombus |
| 2. | Square and Rhombus Formulas |
| 3. | Similarities Between Square and Rhombus |
| 4. | FAQs on Difference Between a Square and Rhombus |
Difference Between Square and Rhombus
A square is a two-dimensional figure that has four equal sides and four equal angles. The sides of a square are perpendicular to each other and its diagonals are of equal length. A rhombus is a quadrilateral in which the opposite sides are parallel and the opposite angles are equal. The sides of a rhombus are not perpendicular to each other and the diagonals of a rhombus are not equal in measure. The following figure helps to identify and differentiate between a square and a rhombus.
Observe the following table that shows the difference between a square and a rhombus.
| SQUARE | RHOMBUS |
|---|---|
| All the angles of a square are equal and measure 90° each. | Only the opposite angles of a rhombus are equal to each other. |
| The diagonals of a square are of equal length. | The diagonals of a rhombus are of unequal length. |
|
A square can be inscribed in a circle. |
A rhombus cannot be inscribed in a circle. |
|
A square has four lines of symmetry. |
A rhombus has two lines of symmetry. |
| The sides of a square are perpendicular to each other. | The sides of a rhombus are not perpendicular to each other. |
Square and Rhombus Formulas
Once we know the length of the sides and the length of the diagonals of a given square and a rhombus, we can use the following formulas to calculate their area and perimeter.
- The formula used to find the area of a square is: Area of a square = s × s, where 's' is the length of the side of a square.
- The formula used to find the perimeter of a square is: Perimeter = 4 × s, where 's' is the length of the side of a square.
- The formula used to find the area of a rhombus is: Area = \(\dfrac{1}{2}\times d_1\times d_2\), where \(d_1\) and \(d_2\) are the lengths of the diagonals.
- The formula used to find the perimeter of a rhombus is: Perimeter = 4 × s, where 's' is the length of the side of a rhombus.
Similarities between Square and Rhombus
Squares and rhombuses have many differences but they are also similar in many ways. The following table shows the similarities between a square and a rhombus.
| SQUARE | RHOMBUS |
|---|---|
| A square is a quadrilateral. | A rhombus is also a quadrilateral. |
| The diagonals of a square bisect each other at right angles. | The diagonals of a rhombus also bisect each other at right angles. |
| The sum of the four interior angles of a square is 360°. | The sum of the four interior angles of a rhombus is 360°. |
| The opposite sides of a square are parallel. | The opposite sides of a rhombus are also parallel. |
| All the sides of a square are of equal length. | All the sides of a rhombus are also of equal length. |
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Solved Examples
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Example 1: Identify if the given parallelogram ABCD is a square or a rhombus if the sides AB, BC, CD, and DA are equal to each other and the interior angles ∠A, ∠B, ∠C, ∠B are all equal to 90°.
Solution: The question mentions that ABCD is a parallelogram.
It is given that the sides AB = BC = CD = DA; and ∠A = 90° , ∠B = 90°, ∠C = 90°, ∠D = 90°
We know the difference between square and rhombus and the fact that all the sides of a square and a rhombus are of equal length. The interior angles of a square are 90°, but the angles of a rhombus are not 90°. Therefore, we can conclude that the given parallelogram is a square.
FAQs on Difference Between Square and Rhombus
What is the Difference Between Square and Rhombus?
The main difference between a square and a rhombus is that all the angles of a square are equal to 90°, and hence are equal in measure, but in the case of a rhombus, only the opposite angles are equal. Apart from this, the diagonals of a square are equal, whereas, the diagonals of a rhombus are not equal in length.
Can a Square be a Rhombus?
Yes, a square comes under the category of a rhombus since it fulfills 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.
Can a Rhombus be a Square?
No, a rhombus cannot be a square unless its diagonals are equal and the interior angles are 90° each.
Are Squares and Rhombuses Parallelograms?
Yes, a square and a rhombus satisfy all the properties of a parallelogram. Therefore, both squares and rhombuses are parallelograms whose opposite sides are parallel and equal to each other, and the opposite angles are of equal measure.
What are Some of the Real-life Examples of a Square and a Rhombus?
A few real-life examples of a square are a chessboard, bread slice, and so on. Some real-life examples of a rhombus are, a kite, car windows, and so on.
What is Common Between a Square and a Rhombus?
There are many similarities between a square and a rhombus.
- Both come under the category of quadrilaterals, so the sum of all the interior angles is 360°.
- The diagonals of both the figures bisect each other at right angles.
- The opposites sides are parallel in both the figures.
- All the sides are of equal length in a square and a rhombus.
What is the Difference Between the Diagonals of Square and Rhombus?
The diagonals of a square are equal, whereas, the diagonals of a rhombus are not equal in length.