how to find perimeter of a square
The perimeter of a square is the total length covered past its boundary, in a plane. Perimeter is the path that encompasses a shape. The perimeter of a closed geometrical shape (2-dimensional) is calculated by adding all the sides together. A square is a four-sided polygon, thus its perimeter of the square will exist equal to the sum of all its iv equal sides. Hither, we have given a detailed explanation of the perimeter of the square, formula and derivation along with solved examples.
What is Perimeter of a Square?
The perimeter of any closed geometrical object is defined as the altitude around that object. The perimeter of a square is the distance covered past its four sides. Perimeter surrounds or outlines the shape in a ii-dimensional plane.
Since all the sides of a square are equal, therefore, the perimeter of square will be 4 times its side, i.east. 4 × Side. It is measured in units, such as grand, cm, in, ft, etc.
Perimeter of Square Formula
The formula to find the perimeter of a square is given beneath:
Perimeter of Square (P) = 4 × Side
Example: If length of side of square is 3cm, and so find its perimeter.
Perimeter of foursquare = iv x side = four x three = 12 cm.
Derivation of Perimeter of Square Formula
The perimeter of the square is defined as the full length of the boundary of a square. Nosotros demand to add all the sides of square to find its perimeter. By the formula of perimeter of polygon, we know;
Perimeter = sum of all sides
Perimeter of square = Sum of the lengths of 4 sides
= side + side + side + side
= four × side
Therefore, the perimeter of Square = 4s units
Where, s = Length of a side of the square
How to Find Perimeter of Square?
We have already learned to summate the perimeter of the square using the formula,
Perimeter = four × side
But if the length of the side of square is not given, then we tin summate the perimeter of square, if two we are given with either of ii details:
- Length of diagonal of foursquare
- Area of square
Let us figure out, how we tin can notice the perimeter using diagonal and using expanse.
Perimeter of Foursquare Using Diagonal
As nosotros know, a foursquare is regular polygon that has all sides equal. As well, all the four angles of square are 90 degrees. Thus, nosotros go the length of diagonal of foursquare, using Pythagoras theorem, as:
Diagonal = Side.√2
Thus, the side of square can be written as:
Side = Diagonal/√2
or
Side of square = √2(Diagonal/2)
As nosotros know,
Perimeter of square = four x side = 4 x √2(Diagonal/two)
Perimeter of square = ii√2(Diagonal) units.
Hence, we tin find the perimeter using diagonal of square.
By using the in a higher place formula, we accept;
Perimeter = ii√ii(Diagonal) = 2√2(10) = 20√2 cm.
Perimeter of Square Using Area
The area of a square is defined as the space occupied by the square. The formula for surface area of square is given by:
Area of a Square = side × side = side² square units
where "s" is the length of one side.
Now, we can write, side of the foursquare w.r.t. surface area,
side = √Area
Hence, the perimeter of square volition be:
Perimeter = 4 x side = 4 √Area units.
Thus, nosotros tin can find the perimeter of a square given its area.
Using the higher up formula, nosotros have;
Perimeter = 4 √Area = 4 √16 = four ten four = sixteen cm.
Related Articles
- Area Of Square Using Diagonals
- Difference between Area and Perimeter
- Perimeter
- Perimeter of a Parallelogram
- Perimeter of Rectangle
- Perimeter of Triangle
Solved Examples on Perimeter of Square
Question one: Find the perimeter of a square whose side is five cm.
Solution:
Given:
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 = twenty cm
Question 2: Calculate the perimeter of a foursquare having a side of xvi cm.
Solution:
Given,
Side of the foursquare = a = sixteen cm
Perimeter of a Square = 4a
= four × 16
= 64 cm
Question 3: If the perimeter of a square is 92 cm, find its side.
Solution:
Perimeter = 4 × side
Or, Side of Square = ¼ × perimeter
So, side of the square = 92/four = 23 cm
Practice Questions on Perimeter of square
- What is the perimeter of square, whose side is equal to 11 cm?
- If length of side of foursquare is v.v cm, then observe its perimeter.
- The length of diagonal of a square is equal to 9 cm. Find its perimeter. (Use: √2 = ane.414)
- If the surface area of foursquare is 100 sq.in., find its perimeter.
Frequently Asked Questions
What is the Perimeter of a Square?
The perimeter of a foursquare is defined as the full distance around the exterior of the square. So, it can exist said that a square'due south perimeter is its full boundary.
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 of the sides volition requite its perimeter. Nosotros tin use also discover the perimeter of square if the length of diagonal or surface area of square is given to us.
What is the Formula for the Perimeter of a Foursquare?
The formula for the perimeter of a foursquare is, P = Side + Side + Side + Side
Or, P = iv × Side
What is the unit of perimeter of square?
Perimeter of foursquare is the total distance enclosed past its sides. Perimeter is measures in units such every bit meters (m), centimeters (cm), inches (in), etc.
What is area of a square?
The area of a square is the region that the foursquare covers in a 2-dimensional space. The area of a square can also exist defined as the number of square units information technology takes to fill the square.
Source: https://byjus.com/maths/perimeter-of-square/
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