Is a Square a Rectangle? Definition, Facts, Examples, FAQs

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Is a Square a Rectangle?

The answer to the question is yes! All squares are rectangles! 

A rectangle and a square are both quadrilaterals. A quadrilateral is a polygon with four sides, four vertices, and four angles. In this article, let’s try to understand why all squares are also considered as rectangles.

What Is the Shape of a Rectangle and Square?

Rectangle and square are two-dimensional, flat-shaped, closed geometric figures. 

Shape and dimensions of rectangle and square

Why Is a Square a Special Type of Rectangle?

Let’s learn the definitions of a square and a rectangle and check if a square fits into the definition of a rectangle.

Definition of Rectangle: A rectangle is a quadrilateral with four right angles. For a quadrilateral to be a rectangle, all four interior angles should measure 90. 

Definition of Square: A square is a quadrilateral with four right angles and four equal sides. 

Since a square has four right angles, it is a rectangle! A square follows all the properties of a rectangle and also has some unique properties of its own.

The key difference between a square and a rectangle is, all sides of a square are equal, whereas only opposite sides of a rectangle are equal.

Square ABCD and rectangle ABCD

Rectangle vs. Square

RectangleSquare
A quadrilateral with four right angles.A quadrilateral with four right angles.
Opposite sides are equal. The longer side measurement is called length. The shorter side measurement is called breadth.All sides are equal in length. 
Diagonals bisect each other.Diagonals bisect each other at right angles.
Diagonals are not perpendicular.Diagonals are perpendicular.
Diagonals are equal.Diagonals are equal.
A rectangle is an irregular polygonA square is a regular polygon.

Properties of Square and Rectangle

PropertyRectangleSquare
SidesOpposite sides are equal.All sides are equal. 
Opposite sides are parallel.

Angles
  All angles are right angles.
Opposite angles are equal.


Diagonals
Diagonals are not perpendicular.Diagonals are perpendicular.
Diagonals bisect each other.
Diagonals are equal.

On comparing the common properties shared between a square and a rectangle, we observe that a square has all the properties that a rectangle has. In other words, we can say that a square can also be referred to as a special type of a rectangle. 

Hence, we can conclude that yes, a square is a rectangle.

How Are Squares And Rectangles Alike?

Properties shared by squares and rectangles:

  • Four interior angles each equal to 90 degrees.
  • Opposite sides are parallel and equal.
  • Two diagonals are equal. 
  • Diagonals bisect each other.

What Additional Properties Distinguish a Square from a Rectangle?

A square has its own unique properties which a rectangle does not have. These properties are

  • All four sides of a square are equal.
  • Diagonals of a square bisect each at right angles. 

Facts about “Is a Square a Rectangle?”

  • A square meets the criteria for being classified as a rectangle, making it a unique type of rectangle.
  • All squares are rectangles, but not all rectangles are squares.
  • Area of a square = (side)2
  • Area of a rectangle = length × breadth
  • Perimeter of a square = side + side + side + side = 4 side
  • Perimeter of a rectangle = length + length + breadth + breadth = 2 × (length + breadth)

Conclusion

In this article, we explored how a square is a special kind of rectangle. We learned the difference, similarities, and comparison points with properties. Let’s solve a few examples and MCQs for better understanding.

Solved Examples on “Is a Square a Rectangle?”

1. What properties are common in both rectangle and square?

Solution: 

Both rectangle and square have the following common properties:

  • All angles are equal and are of 90° each.
  • The opposite sides of both the rectangle and square are parallel and equal.
  • The diagonals of both the rectangle and square are equal. 

2. When does a rectangle become a square?

Solution: 

The key difference between a square and a rectangle is, all sides of a square are equal, whereas only opposite sides of a rectangle are equal.

A rectangle becomes a square when its length equals its breadth. This way all sides become equal in length.

4. A square is formed by joining lengths of two rectangles as given below. What will be the area of the square?

A square formed by joining two rectangles along its length

Solution: 

Side of the square = Sum of widths of the two rectangles

Side of the square = a + b

Area of the square = side ✕ side 

         = (a + b) ✕ (a + b) 

         = a2 + 2ab + b2 square units.

5. A rectangle is divided into two squares given below. What will be the perimeter of the rectangle?

Rectangle formed by joining two squares

Solution: 

Length of rectangle (l) = (a + b) units

Breadth of rectangle (b) = c units

Perimeter of the rectangle = 2(l + b) 

Perimeter of the rectangle = 2(a + b + c) units

Practice Problems on “Is a Square a Rectangle?”

Is a Square a Rectangle? Definition, Facts, Examples, FAQs

Attend this quiz & Test your knowledge.

1

Which of the following is NOT true about a square?

It is a quadrilateral.
It is a regular polygon.
Not every square is a rectangle.
All angles of a square are right angles.
CorrectIncorrect
Correct answer is: Not every square is a rectangle.
Square is a special type of a rectangle. All squares are rectangles.
2

Which of the following is NOT a common property of squares and rectangles?

The diagonals are perpendicular.
The diagonals bisect each other.
The diagonals are equal.
The diagonals of a rectangle bisect each other at 90°.
CorrectIncorrect
Correct answer is: The diagonals of a rectangle bisect each other at 90°.
The diagonals of a rectangle do not bisect each other at 90°.
3

The two dimensions of a quadrilateral are 5 inches and 2 inches. Which could be this quadrilateral?

Square
Rectangle
Rhombus
None of these
CorrectIncorrect
Correct answer is: Rectangle
A rectangle has opposite sides equal. So, there is a possibility that the length are 5 inches and breadth is 2 inches.
4

Are all squares rectangles?

Yes
No
Depends on the lengths of diagonals
Depends on the interior angles
CorrectIncorrect
Correct answer is: Yes
All squares are rectangles.

Frequently Asked Question on “Is a Square a Rectangle?”

Squares are quadrilaterals with 4 congruent sides. Since rhombuses are quadrilaterals with 4 congruent sides, squares are by definition also rhombuses.

No. Not every rectangle is a square. To be a square, all sides of a rectangle must have the same length.

True. A parallelogram in which all the angles are equal is called a rectangle. So, all rectangles are parallelograms. Every rectangle is a parallelogram, but not every parallelogram is a rectangle.

No. All rhombus are not squares. For a rhombus to be a square, all angles should be right angles. A square is a rhombus, but a rhombus is not necessarily a square.

No, rhombus is not a special type of rectangle as rhombus does not have all properties of a rectangle.

A rectangle is not a regular polygon since all sides are not equal. It is only an equiangular polygon.

Yes, every square is a rectangle.