The perimeter of a square is the length that its boundary covers. The perimeter of a square is obtained by adding all the sides together. Here, the concepts about the perimeter of the square, formula and derivation along with solved example questions are covered.
What is the Perimeter of a Square?
The perimeter of any closed geometrical object is defined as the distance around that object. For a square, the perimeter is calculated by adding its four sides. We know that all the sides of a square are equal and hence, its perimeter will be 4 times its side, i.e. 4 × Side.
The formula for Perimeter of a Square
|Perimeter of Square (P) = 4 × Side|
Derivation of a Square’s Perimeter
The perimeter of the square is defined as the length of the boundary of a square.
The Perimeter of the square formula is given by,
Perimeter = sum of the lengths of 4 sides
= side + side + side + side
= 4 × side
Therefore, the perimeter of Square = 4s units
Where, s = Length of a side of the square
|Square Shape in Maths||Construction Of Square|
|Special Parallelograms: Rhombus, Square & Rectangle||Difference Between Square & Rhombus|
|Completing The Square Method||Difference Between Square and Rectangle|
Below is a brief recall about a square and its area.
What is Square?
A square is a quadrilateral in which it has 4 equal sides and all the interior angles of a square are right angles. It is a closed two-dimensional plane figure.
Area of Square
The area of a square is defined as the space occupied by the two-dimensional figure called square and the area of the square formula is given as
Area = width × height
Since width and height are the same, the formula is usually written as
Area of a Square = Side × side = side² square units
where “s” is the length of one side.
Does Square have Surface Area?
People sometimes confuse the area of a square with the surface area. The surface area is, however for three dimensional figures such as a cube where there is more than one surface are involved and not for the planar shapes such as a square having only a single surface.
Thus, to calculate the surface area of the square, one must follow the same method as to compute the area of the square.
Solved Problems Using Perimeter of Square Concept
Question 1: Find the perimeter of a square whose side is 5 cm.
Side, s = 5 cm
The formula to find the perimeter of a square is given by
The perimeter of Square = 4s units
Substitute the value of ‘s’ in the perimeter formula,
P= 4 × 5 cm
P = 20 cm
Therefore, the perimeter of square = 20 cm
Question 2: Calculate the perimeter of a square having a side of 16 cm.
Side of the square = a = 16 cm
Perimeter of a Square = 4a
= 4 × 16
= 64 cm
Question 3: If the perimeter of a square is 92 cm, find its sides.
Perimeter = 4 × side
Or, Side of Square = ¼ × perimeter
So, side of the square = 92/4 = 23 cm
Frequently Asked Questions
What is the Perimeter and Area of a Square?
The perimeter of a square is defined as the total distance around the outside of the square. So, it can be said that a square’s perimeter is its total boundary.
The area of a square is the region that the square covers in a two-dimensional space. The area of a square can also be defined as the number of square units it takes to fill the square.
How to Find the Perimeter of a Square?
To calculate the perimeter of a square, add all the sides of it. There are 4 sides of a square which are all equal in length. The sum will give its perimeter.
What is the Formula for the Perimeter of a Square?
The formula for the perimeter of a square is, P = Side + Side + Side + Side
Or, P = 4 × Side