Difference Between Square and Rectangle
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 as quadrilaterals. Squares and rectangles are the most common shapes seen around us. Apparently, they seem to be quite similar, however, mathematically, they are different. The main difference between them is that a square has all equal sides, whereas, in a rectangle, the opposite sides are equal. In other words, a square is a rectangle in which the adjacent sides are equal and the interior angles are equal to 90°.
|1.||What is a Square and a Rectangle?|
|2.||Important Properties of a Square and a Rectangle|
|3.||Difference Between a Square and a Rectangle|
|4.||Why is a Square Called a Rectangle?|
What is a Square and a Rectangle?
Although squares and rectangles are quadrilaterals, there are certain properties which differentiate them.
A square is a flat two-dimensional shape which has four equal sides, four interior right angles and four vertices.
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°.
Important Properties of a Square and a Rectangle
Some important properties of a square are:
- All the four sides are equal in length.
- All the internal 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.
Some important properties of a rectangle are:
- The opposite sides of a rectangle are equal and parallel to each other.
- All the internal angles of a rectangle are 90°.
- The opposite angles of a rectangle are equal, hence, we also call it a parallelogram.
- The diagonals of a rectangle are of 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.
|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.|
|Shapes formed||A circle can be formed with the point of bisection of the digonals as center of the circle, since all the four vertices are equidistant from the point of bisection.||No such shapes can be formed with the point of bisection of bisection of the diagonals of the rectangle.|
|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|
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 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 the 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 the four sides are equal.
- Diagonals bisect each other at right angles.
Topics Related to Square and Rectangle
Example 1: Find the area of the following shapes with the given measurements.
a) A square with side = 5 units
b) A rectangle with length = 6 units and width = 3 units
a) Side of the square = 5 units
Area of a square = Side × Side
= 5 × 5
= 25 square units.
b) Length = 6 units and width = 3 units
Area of a rectangle = length × width
= 6 × 3
= 18 square units.
Example 2: Find the perimeter of: (i) A square-shaped photo frame with side measuring 10 units and (ii) A rectangular photo frame with a length of 12 units and width of 7 units.
Perimeter of a square = (4 × side)
Side of the square photo frame = 10 units
Therefore, perimeter = 4 × 10
= 40 units
Perimeter of a rectangle = 2 (length + width)
Length = 12 units and width = 7 units
Therefore, perimeter = 2 (12 + 7)
= 38 units
FAQs on Difference Between Square and Rectangle
What Does a Square and a Rectangle Have in Common?A square and a rectangle have the following common properties:
- All the four angles are equal to 90°.
- The diagonals are equal in length.
- Their opposite sides are equal and parallel.
Is a Square a Rectangle and a Rhombus?
A square can be called a rectangle because the interior angles of a rectangle and a square measure 90∘ each, and the opposite sides are parallel and equal. It can also 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 the 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.