measure 90 degrees each, that is, right angles. A square can also be thought of as a special case of rectangle in which two adjacent sides are equal in length.

In this section, we will learn about the square formulas – a list of the formulas related to squares which will help you compute its area, perimeter, and length of its diagonals. They are enlisted below:

Perimeter of square= 4a

Where, a= length of a side of square,

Properties Of Square

1. All its four sides are of equal length.

2. All its four angles are equal in measurements.

3. The two diagonals cut into each other at right angles, that is 90°.

4. Two opposite sides of a square are parallel and equal in length.

5. Diagonals of a square are equal.

Derivations:

A square with the lengths of its side and diagonal are a and d units respectively.

Formula for area of a square: 

Area of a square is the region which is enclosed within its boundary. As we mentioned, a square is nothing but a rectangle with its two adjacent sides being equal in length. Hence, we express area as:

Area of a rectangle = Length × Breadth

Here,

Formula of perimeter of a square:

Perimeter of a square is the boundary of its length. The sum of length of all sides of a square shows its boundary. Therefore, the formula can be written as:

Perimeter = length of 4 sides

= a + a + a + a

= 4a

Perimeter of square= 4a

Formula of diagonal of a square: 

Diagonal of the square is a line that connects two opposite sides in a polygon. To determine the length diagonal of a square, we use the Pythagoras Theorem.

In the diagram shown below, 'diagonal' splits the square into two right angled triangles. It is observed here that since a square has equal length for adjacent sides, the right angled triangle is also isosceles in which each of its sides measures 'a' units.

Hence we could easily apply the Pythagorean theorem on these triangles with the base and perpendicular as 'a' units and hypotenuse as' units.

Solved example

Q1: A square has one of its sides measuring 23 cm. Calculate its area, perimeter, and length of its diagonal.

Solution: Given,

Side of the square = 23 cm

Area of the square 

Perimeter of the square= 4a= 4 × 23 = 92 cm

Diagonal of square

Q2:  A rectangular floor is 50 m long and 20 m wide. Square tiles, each of 5 m side length, are to be used to cover the floor. Determine the total number of tiles that will be needed for flooring.

Solution: Given,

Length of the floor = 50 m

Breadth = 20 m

Area of the rectangular floor = length x breadth = 50 m x 20 m = 1000 sq. m

Side of one tile = 5 m

Area of one such tile = side x side = 5 m x 5 m = 25 sq. m

Other Related Sections

NCERT Solutions | Sample Papers | CBSE SYLLABUS| Calculators | Converters | Stories For Kids | Poems for Kids| Learning Concepts | Practice Worksheets | Formulas | Blogs | Parent Resource