Perimeter and Area of Square

Perimeter and Area of Square

All four sides of a square are equal and each of its internal angles is right-angled. 

A square's perimeter is equal to the sum of the length of all sides of its border. Simply put, the perimeter of a square is calculated by summing the lengths of all its sides. The perimeter of the square, its formula, and derivation, as well as answered example problems, are discussed in this section.

Finding Perimeter of a Square

The perimeter is equal to the sum of the lengths of the four sides.

The perimeter is equal to the sum of the lengths of the four sides. Perimeter = Add the lengths of 4 sides = Side 1 + Side 2 + Side 3 + Side 4.

Now, all sides of a square are the same. 

Let side = x

Therefore,

Perimeter  = x + x + x + x = 4x Units

As a result, the perimeter of Square is equal to 4x units. A closed geometrical object's perimeter is defined as the distance surrounding it. The perimeter of a square is determined by summing its four sides. Given that all of a square's sides are equal, its perimeter will be four times its side, i.e. 4x.

# How to find the length of a side when the perimeter of a square is given?

If “P” is the perimeter, and s is the length of a square respectively. Then,

Length of the Square (s) = P/4

Area of a square:

Consider a square with a side of 's' unit.

Hence, the square’s area is given by: 

Area (sqaure)  = s x s

Therefore, Area (A) = s^2 square units.

How to find the length of a side when an area of a square is given?

 If “A” is the area, and s is the side of the square respectively. Then,

Length (s) = = √A.

Diagonal of the square: The diagonal of a square follows the Pythagoras theorem. That is, the diagonal is equal to the sum of squares of the remaining two sides. If s is the side of a square, then diagonal (d) = a^2 + a^2. Here, the “^” symbol refers to power. 

Length of the diagonal = √(s² + s²) = √(2s²^2) = s√2 units

Problems

Q1) Find the perimeter of the square if the side is 2m respectively.

Answer 1) Initially, let us draw a diagram of a square with side 2m respectively.

Perimeter =  4 x side (or s+s+s+s) = 4 x 2 = 8m

Q2) Find the length of the square if the perimeter is 8 respectively.

Answer 2) Now the formula to find the length of a square when the perimeter is given below by:

S = P/4 = 8/4 = 2 m

Q3) Find the area of the square if the length of the side is 2m respectively.

Answer 3) The formula for the area of a square is given by:

Area (Square)  = side x side = Side ^ 2

Here Side  = 2

Therefore, Area of Sqaure = 2 m x 2 m = 4 m^2 (or 4 meter square)

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