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

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. 

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.

Rectangle vs. Square

Rectangle	Square
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 polygon.	A square is a regular polygon.

Properties of Square and Rectangle

Property	Rectangle	Square
Sides	Opposite 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?”

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?

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?

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?”

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