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Square and Rhombus both fall under a similar category of shapes which are called quadrilaterals meaning (figures with 4 sides) and the main difference between square and rhombus is on the basis of angles. In square all the angles within the figure are equal to 90 degrees and all the 4 angles are same but in the case of rhombus only the opposite angles of the figure are same and equal in measurement, the angles within the rhombus are not equal to 90 degrees. Every square can be called a rhombus but not every rhombus is necessarily a square. It has to fulfil certain conditions to be recognized as a square.
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Key Takeaways: Quadrilaterals, Diagonals, Perpendicular, Parallelogram, Symmetry, Perimeter, Bisection
Square
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A square is a two-dimensional figure with 4 sides and angles and hence it falls under the quadrilateral category. All the angles and sides of a square is known to be the same with sides perpendicular to each other which forms 90°.
Some properties of a square are: -
- All the interior angles measure 90°
- All the sides are equal to each other and hence considered as congruent.
- The opposite sides are parallel as well as equal to each other.
- The 2 diagonals of a square are equal in length and bisect each other at 90 degrees
- Equal diagonals of a square form 2 isosceles triangles.
- Perimeter of a square is 4a where ‘a’ is each sides length.
- Area of a square is ‘a2’ units square where sides measure ‘a’ unit length
Also Read: Difference Between Area and Perimeter
Rhombus
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A Rhombus is considered as a special parallelogram and it is also often called as Diamond or Rhombus Diamond. In a rhombus opposite angles and sides are equal and the opposite sides are parallel to each other. There are 2 diagonals present in rhombus and are different from each other. It is known as Rhombi or rhombuses in plural form.
Some properties of Rhombus: -
- Opposite sides are equal and parallel to each other.
- Diagonals are different in length and they bisect each other at 90°.
- Circumscribing and inscribing cannot be made around a rhombus.
- Diagonals of a rhombus are known to bisect its angles.
- 2 adjacent (near) angles of a rhombus have a sum of 180°.
A square is considered as 2-dimensional figure which has 4 equal sides and all the angles within the figure are all the same and equal which measures to 90°. The sides of square are known to be perpendicular to each other which mean all the sides form right angle (90°) with the other side’s which is the reason for equal within the square. On the other hand, rhombus is special type of parallelogram which also falls under the category of quadrilaterals. The sides of rhombus are not perpendicular to each other and also the diagonals of rhombus are not equal.
Also Read: Area of Rhombus
Similarities between Square and Rhombus
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The following table enlists few key similarities between a Square and a Rhombus:
| Square | Rhombus |
| Falls under the category of quadrilaterals | Falls under the quadrilateral category and is a special case of parallelograms. |
| All the sides are equal in length | Length of the sides are equal |
| Opposite sides and angles are equal | In Rhombus only the opposite angles and side are equal |
| Diagonals are perpendicular to each other | Diagonals of rhombus also form perpendicular with each other (forms 90°) |
| Sum of all the angles within or interior angle sum is 360° | In rhombus the interior angle sum is also 360° |
| Square with side length ‘a’ have their perimeter as 4a units | Rhombus too have a perimeter of 4a units with side length ‘a’ |
Differences between Square and Rhombus
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The following table enlists key differences between a Square and a Rhombus:
| Square | Rhombus |
| In a square all the angles are equal and measure to 90° | In a Rhombus only the angles opposite to each other are equal. They can measure to 90° or not |
| The diagonals present in square are equal in length | The diagonals of a rhombus are un equal in length. |
| A square can be inscribed (drawn inside) a circle | A rhombus however cannot be inscribed in a circle. |
| A square is known to have 4 lines of symmetry (divided into 2 equal parts) | A rhombus is said to have only 2 lines of symmetry |
| Sides of a square is perpendicular to each other(forms 90° with each other) | Sides of a rhombus do not form perpendicular with each other. |
| The area of square is a2 units with sides measuring ‘a’ | Area of a rhombus is half the product of their diagonals. |
Square and Rhombus Formulae
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- 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 = 1/2×d1×d2,
where d1 and d2 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.
Also Read: Types of Polygons
Things to Remember
- Every square is a rhombus but vice versa may not be true at all times. However, both are considered as quadrilaterals and rhombus is often considered as a special parallelogram.
- In square all sides and angles are equal. Each angles measure 90 degree and the sum of interior angles are 360°
- In rhombus opposite sides and angles are equal. Sum of interior angles are 360 degree and the sum of 2 adjacent angles are 180°
- Area of square is product of their sides whereas the area of rhombus is half the product of their diagonals.
Sample Questions
Ques 1: Can a rhombus be a square? (1 marks)
Ans.: A rhombus can only be a square when both of its diagonals are of same length and each interior angles measures 90°
Ques 2: Can a square be a rhombus? (1 marks)
Ans.: A square is already considered as a rhombus because it fulfils all the properties of a rhombus. Opposite sides and angles are equal. Opposite sides are parallel and the diagonals are perpendicular to each other
Ques: Give some real life examples for square and rhombus? (1 marks)
Ans.: Chessboard is a common example for square whereas kite is a common example for rhombus.
Ques: Write the similarities between square and rhombus? (3 marks)
Ans.: Sum of the interior angles are 360°, diagonals of the figures bisect each other forming right angle. Opposite sides are parallel.
Also Read:
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