Difference Between Square and Rectangle
The difference between a square and a rectangle is that a square has all equal sides, whereas, in a rectangle, the opposite sides are equal. In geometry, there are many shapes like circles, triangles, squares, rectangles, cubes, cones, cylinders, and so on. Among these, the figures that have four sides are termed quadrilaterals. Squares and rectangles are the most common shapes seen around us. Apparently, they seem to be quite similar, however, mathematically, they are different. In other words, a square is a rectangle in which the adjacent sides are equal and the interior angles are equal to 90°.
What is a Square and a Rectangle?
Although squares and rectangles are quadrilaterals, there are certain properties that differentiate them.
Square
A square is a flat two-dimensional shape (2D shape) that has four equal sides, four interior right angles, and four vertices.
Rectangle
A rectangle is a two-dimensional shape in which the opposite sides are equal. It has four equal angles and four vertices. All the four angles of a rectangle measure 90°.
Properties of a Square and a Rectangle
The important properties of a square and a rectangle are given below. Observe the figure given below to identify and differentiate between the two figures.
Properties of a Square
- All four sides of a square are equal in length.
- All the interior angles of a square are 90°.
- The opposite sides of a square are parallel to each other.
- The diagonals of a square are equal in length and they bisect each other.
Properties of a Rectangle
- The opposite sides of a rectangle are equal and parallel to each other.
- All the interior angles of a rectangle are 90°.
- The diagonals of a rectangle are of the same length and bisect each other.
Difference Between a Square and a Rectangle
The important differences between a square and a rectangle are listed in the table given below.
Square vs Rectangle
| Property | Square | Rectangle |
|---|---|---|
| Sides | A square has four equal sides. | In a rectangle, the opposite sides are equal. |
| Diagonals | The diagonals of a square bisect each other at 90°. | The diagonals of a rectangle bisect each other at different angles. One angle is an obtuse angle and the other one is an acute angle. |
| Area | The area of a square is measured using the formula: Area = Side × Side | The area of a rectangle is measured as the product of its length and width. Area = Length × Width |
| Perimeter |
The perimeter of a square is calculated by using the formula: Perimeter = 4 × Side |
The perimeter of a rectangle is calculated by using the formula: Perimeter = 2 (length + width) |
| Length of the diagonal |
As per the Pythagoras theorem (Pythagorean theorem), the length of the diagonal of a square is the product of the square root of 2 and the side of the square. Length of diagonal = √(2 × Side) |
As per the Pythagoras theorem (Pythagorean theorem), the length of the diagonal of a rectangle is the square root of the sum of squares of the length and width. Length of diagonal = √(Length2 + Width2) |
Why is a Square Called a Rectangle?
We call a square a special type of rectangle because they both share some common properties which are listed below.
- A square and a rectangle have interior angles equal to 90°.
- The opposite sides in both shapes are equal and parallel.
- The diagonals that bisect each other are equal in length.
Here are some properties that do not apply to rectangles and are found only in squares.
- All four sides are equal.
- Diagonals bisect each other at right angles.
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What is the Difference Between a Square and a Rectangle?
The important points of differences between a square and a rectangle:
- A square has four equal sides, whereas, in a rectangle, the opposite sides are equal.
- The diagonals of a square bisect each other at 90°, whereas the diagonals of a rectangle bisect each other at different angles.
What are the Similarities Between Square and Rectangle?
A square and a rectangle have the following similarities:
- All four angles are equal to 90°.
- The diagonals are equal in length.
- Their opposite sides are equal and parallel.
Which Property of Square is Different from the Property of Rectangle?
The property of a square that makes it different from a rectangle is that in a square all four sides are equal and parallel, whereas, in a rectangle, only the opposite sides are equal and parallel.
Is a Square a Rhombus?
A square can be called a rhombus because it fulfills the properties of a rhombus which has four equal sides and its opposite sides are parallel to each other.
Is a Square a Rectangle?
Yes, a square is a rectangle because it possesses all the properties of a rectangle. Its opposite sides are parallel and equal and the interior angles are 90∘ each. Hence, a square can be called a special type of rectangle.
Can a Rectangle be a Square?
Since a rectangle does not have all four sides of equal measure, it cannot be a square.
What are the Important Properties that Confirm that a Square is a Rectangle?
The properties listed below confirm that a square is a rectangle:
- A square has all its interior angles equal to 90°.
- The opposite sides of a square are equal and parallel.
- The diagonals bisect each other and are of equal length.