Content Curator
In Geometry, there are shapes that have four sides which are termed as quadrilateral. Squares and rectangles are the most common example of quadrilateral shape. 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, a rectangle has equal opposite sides. In other words, a square is a rectangle in which the adjacent sides are equal and the interior angles are equal to 90°.
| Table of Content |
Key Takeaways: Square, Rectangle, Difference between Square and Rectangle, Area and Perimeter of Square, Area and Perimeter of Rectangle, Characteristics
Definition of Square and Rectangle
[Click Here for Sample Questions]
Square: A square is a closed two-dimensional plane figure with four equal sides, four interior right angles and four vertices. Since all the angles are of equal measure, it is considered as an equiangular quadrilateral.
Rectangle: A rectangle is a two-dimensional quadrilateral with four sides. The opposite side of a rectangle is parallel to each other. It means that the opposite faces of the rectangle are of equal measure. A rectangle has four angles, each measuring about 90° and four vertices. As like square, a rectangle is also called an equiangular quadrilateral.
Also Read: Difference Between Area and Perimeter
Difference between Square and Rectangle
[Click Here for Sample Questions]
| Property | Square | Rectangle |
| Sides | A square has four equal sides. | A rectangle has equal opposite sides. |
| Diagonals | The diagonals of a square bisect each other at 90°. | The point where diagonals of a rectangle bisect each other form one obtuse angle and the other an acute angle. |
| Shapes formed | A circle can be formed with the point of bisection of the diagonals as the centre of the circle since all the four vertices are equidistant from the point of bisection. | With the point of bisection of the diagonals of the rectangle No such shapes can be formed. |
| Area | The area of a square is measured using the formula: Area = Side × Side = Side2 | The area of a rectangle is measured as the product of its length and width. Area = Length × Breadth |
| 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 + breadth) |
| Length of the diagonal | As per the Pythagoras 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 = \(\sqrt{2} \) × Side | As per the Pythagoras 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 = \(\sqrt{(Length^2 + Width^2)}\) |
Characteristics
[Click Here for Sample Questions]
Square:
- Length of all four sides is equal.
- All the internal angles of a square are 90°.
- The square has opposite sides parallel to each other.
- The square has equal length diagonals which bisect each other.
Rectangle:
- The rectangle has only opposite sides equal and parallel to each other.
- The internal angles of a rectangle are all of the measure 90°.
- Rectangle is a parallelogram since, opposite angles of a rectangle are equal.
- The diagonals of a rectangle are of the same length and bisect each other.
Also Read: Prime numbers
Why a Square is also called a Rectangle?
[Click Here for Sample Questions]
A square is called a special type of rectangle because they both share some common properties:
- The interior angles of a square and a rectangle are of measure 90°.
- Both the shapes have equal and parallel opposite sides.
- The diagonals that bisect each other are equal in length.
Also Read: BODMAS Rule
Things to Remember
- Square and Rectangle share few common properties such as interior angles are 90°. opposite sides are parallel and equal.
- Diagonals of square and rectangle bisect each other and are equal in length.
- Area of Square = Side2 and Area of Rectangle = Length x Breadth
- Perimeter (Square)= 4(Side) and Perimeter (Rectangle)= 2(Length + Breadth).
- Rectangle has opposite sides equal; however, square has all the sides equal, hence, square is called special type of rectangle.
Sample Questions
Ques: Find the area of the following shapes with the given measurements. (4 marks)
a. A square with side = 5 units
b. A rectangle with length = 6 units and width = 3 units
Solution:
- 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.
Ques: Find the perimeter of (4 marks)
a. A square-shaped photo frame with a side measuring 10 units and
b. A rectangular photo frame with a length of 12 units and width of 7 units.
Solution:
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
Ques: Find the perimeter of the following figures: (2 marks)
Solution:
- Perimeter of the rectangle = 2(l + b) = 2(8 + 6) = 2 × 14 = 28 cm
- Perimeter of the square = 4 × side = 4 × 6 = 24 cm
Ques: The length and breadth of a rectangle are 10 cm and 8 cm respectively. Find its perimeter if the length and breadth are (i) doubled (ii) halved. (3 marks)
Solution:
Length of the rectangle = 10 cm
Breadth of the rectangle = 8 cm
- When they are doubled,
l = 10 × 2 = 20 cm
b = 8 × 2 = 16 cm
Perimeter = 2(l + b) = 2(20 + 16) = 2 × 36 = 72 cm
- When they are halved,
l = 10/2 = 5 cm
b = 8/2 = 4 cm
Perimeter = 2(l + b) = 2(5 + 4) = 2 × 9 = 18 cm
Ques: The area of a rectangle is 544 cm2. If its length is 32 cm, find its breadth. (2 marks)
Solution:
Area = 544 cm2
Length = 32 cm
Breadth of the rectangle = Area/ Length
= 544/32
= 17 cm
Hence, the required breadth = 17 cm
Ques: If the side of a square is doubled then how much time its area becomes? (2 marks)
Solution:
Let the side of the square be x cm.
Area = Side2 = x2 sq. cm
If its side becomes 2x cm then area = (2x) 2 = 4x2 sq. cm
Ratio is x2:4x2 = 1:4
Hence, the area would become four times.
Ques: The areas of a rectangle and a square are equal. If the length of the rectangle is 16 cm and breadth is 9 cm, find the side of the square. (2 marks)
Solution:
Area of the square = Area of the rectangle = 16 × 9 = 144 cm2
Side of the square = √Area of the square = √144 = 12 cm
Hence, the side of square = 12 cm.
Ques: Construct a square ABCD, each of whose diagonals is 5.2 cm. (3 marks)
Solution:
Steps of Construction:
- Draw AC=5.2 cm
- Draw the right bisector XY of AC, meeting AC at O.
- From O set off OB = (1/2)*5.2cm = 2.6cm along OY and OD = (1/2)*5.2cm = 2.6cm along OX.
- Join AB, BC, CD and DA.
ABCD is the required square.
Also Read:
Comments