Perimeter of Square Formula: Derivation, Explanation and Solved Examples
The perimeter of square formula any enclosed geometric figure is the measure of the total distance around that figure. In the case of a square, the perimeter corresponds to the combined length of its four sides.
Anchal Singh16 Sept, 2023
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The perimeter of square Formula represents the overall length of its boundary within a two-dimensional plane. It essentially outlines the path encircling the shape. To calculate the perimeter of a closed geometric figure, such as a square, you simply add up the lengths of all its sides. Since a square is a four-sided polygon with all sides of equal length, its perimeter is determined by summing up the measurements of all four sides. In this explanation, we will provide a comprehensive overview of how to calculate the perimeter of a square, including the formula, derivation, and illustrated examples.
What Is The Perimeter of Square Formula?
The perimeter of any enclosed geometric figure is the measure of the total distance around that figure. In the case of a square, the perimeter corresponds to the combined length of its four sides. Perimeter essentially defines the boundary of the shape within a two-dimensional plane. Since all sides of a square are of equal length, the square's perimeter is four times the length of one side, expressed as 4 × Side. Perimeter is typically measured in units such as meters (m), centimeters (cm), inches (in), feet (ft), etc. The formula for calculating the perimeter of a square is as follows:
Also Check - Volume of a Cube Formula
Derivation Of The Perimeter Of Square Formula:
The perimeter of a square is defined as the total length of its boundary. To find the perimeter, we need to add up all the sides of the square. Using the formula for the perimeter of a polygon, we know that: Perimeter = Sum of all sides For a square, this translates to: Perimeter of square = Sum of the lengths of 4 sides = side + side + side + side = 4 × side Therefore, the formula for the perimeter of a square is given as: Perimeter of Square = 4s units Where: s = Length of one side of the squareAlso Check - Volume of a Cylinder Formula
How To Calculate The Perimeter of Square
We have already learned how to calculate the perimeter of a square using the formula: Perimeter = 4 × side But if you are not given the length of the side, you can still find the perimeter if you have either of these two pieces of information: Length of the diagonal of the square Area of the square Let's explore how to find the perimeter using these two pieces of information.Also Check - Volume of a Hemisphere Formula
Perimeter Of Square Using Diagonal
A square is a regular polygon with all sides equal, and all four angles are 90 degrees. You can find the length of the diagonal of a square using the Pythagorean theorem: Diagonal = Side × √2 Therefore, the side of the square can be expressed as: Side = Diagonal / √2 or Side of square = √2(Diagonal / 2) Since we know that: Perimeter of square = 4 × side = 4 × √2(Diagonal / 2) Perimeter of square = 2√2(Diagonal) units For example, if you want to find the perimeter of a square with a diagonal length of 10 cm: Perimeter = 2√2(Diagonal) = 2√2(10) = 20√2 cmAlso Check - Perimeter of a Triangle Formula
Perimeter Of Square Using Area
The area of a square represents the space it occupies. The formula for the area of a square is given by: Area of a Square = side × side = side² square units Here, "s" is the length of one side. You can express the side of the square in terms of its area as: Side = √Area Hence, the perimeter of the square can be calculated as: Perimeter = 4 × side = 4 √Area units For example, if the area of a square is 16 sq. cm: Perimeter = 4 √Area = 4 √16 = 4 × 4 = 16 cmSolved Examples On Perimeter Of Square
Question 1: Determine the perimeter of a square with a side length of 5 cm.Solution:
Given:
Side length, s = 5 cm The formula for calculating the perimeter of a square is as follows: Perimeter of Square = 4s units Now, substitute the value of 's' into the perimeter formula: P = 4 × 5 cm P = 20 cm Hence, the perimeter of the square is 20 cm. Question 2: Compute the perimeter of a square with a side length of 16 cm.Solution:
Given:
Side length of the square = a = 16 cm The formula for the perimeter of a square is: Perimeter of Square = 4a Substitute the value of 'a' into the formula: Perimeter = 4 × 16 Perimeter = 64 cm Therefore, the perimeter of the square is 64 cm. Question 3: If the perimeter of a square is 92 cm, determine the length of its side.Solution:
Perimeter = 4 × side To find the side length, rearrange the formula as follows: Side of Square = Perimeter / 4 Now, calculate the side length: Side of the square = 92 cm / 4 Side of the square = 23 cm So, the side length of the square is 23 cm.Perimeter of Square Formula FAQs
What Does the Perimeter of a Square Represent?
The perimeter of a square is the complete distance around the outer boundary of the square. Essentially, it signifies the total length of the square's boundary.
How Can the Perimeter of a Square Be Calculated?
To determine the perimeter of a square, you simply add up the lengths of all its sides. A square has four sides, all of which are equal in length. Summing up these sides gives you the perimeter. Alternatively, you can also find the perimeter of a square if you are provided with the length of its diagonal or its area.
What Is the Mathematical Formula for Calculating the Perimeter of a Square?
The formula for calculating the perimeter of a square is as follows:
Perimeter (P) = Side + Side + Side + Side
Or, more concisely:
P = 4 × Side
In What Units Is the Perimeter of a Square Measured?
The perimeter of a square represents the total distance enclosed by its sides. Therefore, it is measured in units such as meters (m), centimeters (cm), inches (in), and so on, depending on the context and the system of measurement used.
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