A quadrilateral which is a four-sided closed polygon, with all sides and angles equal in measurement and with opposite sides parallel to each other is a square. The diagonals of a square are also equal bisecting each other at right angles (90 degrees). The sum total of all the four sides is the perimeter of square whereas the region bounded by the shape gives the area of the same. Both the concepts are important and find application in the construction and finding out the cost of tiling a square plot, fencing a square garden, the perimeter of any footpath around any park, or the area of the flooring etc. Thus, these have wider application in one’s daily routine and life. In this article, we will understand the concept of the perimeter of the square in the easiest possible way.

## The Perimeter of the Square

As it is known that the perimeter of any figure is calculated by adding up all the sides of the respective figure. Similarly, the perimeter of the square is defined as the measurement of the complete boundaries or outlines surrounding the shape or region.

Since all the four sides of the square are equal hence the perimeter of the same can be four times the size of one side.

The formula for the same symbolically can be represented as:

**The perimeter of the square= 4 × side of the square.**

## Derivation of the Formula of the Perimeter of the Square

Perimeter is the sum of all sides. Then perimeter of a square= side+ side+ side+ side= 4× side

If each side of the square is ‘a’ unit.

Then, perimeter= a+ a+ a+ a (since all sides of square are equal)

Hence P= 4×a or 4a.

If the side length of a square is given then the formula mentioned works. But, in case it isn’t given, the problem of calculating the perimeter can be sorted with the help of the length of the diagonals or the area of the figure, whatever is provided.

**The derivation with the help of the measurement of diagonal**

A polygon that is regular owns equal sides. It’s already understood that each angle of a square is 90 degrees. One can use the Pythagoras theorem to find out the side of the square. Here the sides are equal and the diagonals resemble the hypotenuse of the right triangle giving the formula, Diagonal^2= 2*side.

This implies that **the Side of the square= Diagonal√2**

Already it’s clarified above that Perimeter of square= 4* side

Substituting the value of side, the formula becomes, **Perimeter= 4*Diagonal√2**

Thus, the perimeter of the square is obtained when only the diagonal of the square is known.

**The derivation of the perimeter of a square figure if the only area is given.**

Since the area of square is the region bounded by the perimeter of the figure, a little logic and understanding may ensure the calculation of the perimeter of the square using the area of the same.

**Area of square= **side* side= side^2

Then **side of square= √Area**

Again, substituting the value of side in the formula of the perimeter, we get **Perimeter of the square= 4*√Area of the square.**

This is the formula for calculating the perimeter of the square when only the area of the figure is provided. In simplest words, the total distance around the square area or that enclosed within its sides is the perimeter of the same.

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