Rectangle in Maths

Last Updated : 30 Jan, 2026

A rectangle is a two-dimensional flat shape. It is mainly a quadrilateral with four sides and the following properties.

  • All four angles are right angles (90°).
  • The opposite sides of a rectangle are equal in length and parallel to each other.
  • The longer side of the rectangle is called the length of the rectangle.
  • The shorter side of the rectangle is called the breadth of the rectangle.
rec_2
Rectangle showing equal sides and right angles

Also, since its opposite sides are equal and parallel, a rectangle is a type of parallelogram.

Some of the real-life examples are

rectangular_shaped_objects
Many everyday objects are rectangular in shape.

Area of a Rectangle

Area is the space covered by a two-dimensional shape on a flat surface.

rec

The formula of area of a rectangle is: Area = length × width

Example: Area of the rectangular photo frame whose sides are 8 cm and 6 cm.

Length × Breadth = 6 × 8 = 48 cm2

Perimeter of a Rectangle

The perimeter of a rectangle is the total length of its boundary. It is found by adding the lengths of all four sides of the rectangle and is measured in units of length, such as centimetres or metres.

rec_3

The formula for the perimeter of a rectangle is: Perimeter (P) = 2 × (Length + Width)

Example: Perimeter of the rectangular field whose sides are 9 m and 13 m.

Perimeter = 2 × (l + b)
= 2 × (9 + 13) = 2 × (22) = 44 m

Diagonal of a Rectangle

A rectangle has two diagonals, that bisects each other. Both the diagonals are equal in length.

diagonals_of_a_rectangle
Diagonals of a rectangle are equal

Each diagonal divides the rectangle into two right-angled triangles. Because of this, we can find the length of the diagonal using the Pythagoras theorem.

The formula for the length of the diagonal of a rectangle is:

D = √(L² + W²)

where D is the diagonal, L is the length, and B is the breadth of the rectangle.

Example: Length of the diagonal of the rectangle whose sides are 6 cm and 8 cm.

Length of diagonal (d) = √( l2 + b2)

d = √( 82 + 62) 
d = √ (64 + 36) = √(100)
d = 10 cm

Thus, the length of the rectangle is 10 cm

Golden Rectangle

A golden rectangle is a special type of rectangle in which the ratio of length to width follows the golden ratio. This ratio is equal to 1 : (1 + √5) / 2, which is approximately 1 : 1.618. This means the length of the rectangle is about 1.618 times its width.

rec4
Golden rectangle divided into proportional sections

For example, if the width of a golden rectangle is 1 unit, then its length will be about 1.618 units.

Learn in detail

Comment

Explore