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Perimeter of Square – Definition, Formula, Examples

perimeter of square

Have you observed the shapes around you? Everything in our surroundings has a shape. For example, have you seen a photo frame? Can you tell its shape just by looking at it? Well, it should not be difficult. Its shape can either be square, rectangle, circle, or oval.

No matter the shape, they always have a boundary like that of the photo frame. If you were to wrap a sheet of paper around the periphery of the photo frame, you would get the perimeter of that shape. 

One can apply this logic in daily life also. For instance, if you were to walk around a square-shaped park, the area you would cover by walking around its boundary would be equal to the perimeter of the park. Knowing this, one can easily understand how much they walk while in the park. Keep reading to understand what a perimeter is.

What is the perimeter of a shape? 

A shape has a particular boundary that encloses the complete structure when we look at a figure. Be it a box, a frame, a park, or a building. Every design is held within a limit known as the perimeter.

When we talk about the perimeter of a shape, it is referred to the total length of its boundary. However, a perimeter is only a two-dimensional geometric shape.

One can easily calculate the perimeter of a shape by knowing the length of each side of that particular shape. For example, if you want to draw the boundary of your book, which is rectangular, you would be able to do this by measuring each side and adding together. By adding the length of each side of the book, one can easily know the perimeter of the boundary of the book.

What do you understand about the perimeter of a square?

After knowing what the perimeter of a shape is, it will be easy to understand the perimeter of the square.

The perimeter of a square is the area that covers the boundary of a square-shaped object. For example, if one rides a bicycle around a square-shaped park, to find out the area they covered will be equal to the perimeter of that particular park.

Another example can be a square table. If a person wants to decorate the boundary of the square table with a ribbon, then the total length of the ribbon needed by them will be equal to the perimeter of the table. The frame of a square is the total sum of the lengths of its four sides.

The perimeter of a square: Formula

The perimeter of a square is calculated as the sum of the lengths of its four sides. Since all sides of a square are equal, one can multiply one side four times to calculate its perimeter.

If a square has a side of length A, the perimeter will be four times A.

The perimeter of square= 4 × A

Therefore,

The perimeter of square= 4 × Side

What are the advantages of knowing the perimeter of the square?

There are various advantages of knowing the perimeter of not only a square but also of other shapes. 

By knowing the perimeter of a shape, or in this case of a square, one can also calculate the length of each side. It means that if the perimeter of a square shape is 12 cm, one can easily calculate the side by dividing it by 4.

For example,

Perimeter= 12 cm

Length of one side= X

Perimeter= 4 × X

12 = 4 × X

X = 12/4

X = 3 cm

Apart from this, one advantage of knowing the perimeter of a square is that you can also calculate the area of a square.

From the above calculation, it is clear that one can calculate the unknown side of a square if the perimeter is known. And if one side is known, it will be easy to calculate the area, i.e., side × side.

The perimeter of square: Derivation

The perimeter of a square is the area that covers the total length of the boundary of that square. One can easily define the perimeter of a square as a border that encloses a space inside it. 

To find out the perimeter of a Polygon, one can do it by a simple formula.

Perimeter = sum of all the sides of a polygon

Therefore,

The perimeter of a square = sum of all the sides of the square

Perimeter of a square = side + side + side + side (a square has four sides)

The perimeter of a square = 4 × side

How to find out the perimeter of a square?

From the above derivation, it is clear that the sum of lengths of all the sides of a square gives the perimeter of the square.

It would be important to note that even if one side of a square is known and the rest of the three sides are unknown, it is still possible to calculate the perimeter of the square.

It is because a square has four sides that are equal in length. So, by knowing the length of just one side, it is possible to calculate the perimeter of the whole square.

For example, if one side of a square is 16 cm, then its perimeter will be-

Perimeter of a square = 4 × side

Perimeter of a square = 4 × 16

The perimeter = 64 cm

How to use diagonal to calculate the perimeter of a square?

A square is a Polygon that has all sides equal in mathematical terms. It means each side of a square makes a right angle (90°) at their point of intersection.

This information can help one calculate the perimeter of a square. When there is a diagonal in a square, it divides the square into two halves. These halves become two right-angled triangles. Thus, sharing all the properties of a right-angle triangle.

In this case, the diagonal becomes the hypotenuse. So, by Pythagoras theorem, one can use the hypotenuse to calculate the side of a square.

Thus, 

Diagonal = hypotenuse

Side = Diagonal/√2

How to calculate the perimeter of a square by its area?

An area of a square is referred to the area enclosed within its perimeter. In other terms, an area is a space occupied by a Polygon.

Talking about the area of a square, one can calculate it by multiplying one side with its other side. However, because each side is the same length, one can calculate its area by squaring one of its sides.

For example, if one side of a square is 4 cm, then its area will be,

Area of the square = side × side

Or,

Area of the square = (side)²

 = 4²

 = 16 cm²

Now that it is easy to calculate the area of a square, it would be effortless to extract the perimeter when its area is given.

Suppose the area of a square is 25 cm². And you are asked about calculating its perimeter. The steps are pretty simple.

  • Calculate the value of one side by doing a square root of the area
  • After getting the length of one side, multiply it by 4
  • After multiplying the one side by 4, you get the perimeter of a square

Calculation:

Area of the square = 25 cm²

One side of the square = √area of square

One side of the square = √25

Length of one side = 5 cm

Now, if one side of the square of 5 cm, its perimeter will be,

The perimeter of the square = 4 × side

The perimeter of the square = 4 × 5

Perimeter = 20 cm

Some solved questions dealing with the calculation of the perimeter of the square

Sample 1: The perimeter of a square is 16 cm. What will be the length of each side?

Calculation:

The perimeter of the square is 16 cm.

Let the side length be ‘x’ cm.

The perimeter of a square = 4 × (side)

16=4×(x)

x = 4 cm

Sample 2: If the side “a” is = 2 cm in a square. What will be the lengths of b, c, and d?

Calculation:

Side “a” of the square is = 2 cm.

We use the property of a square that explains that all the sides of a square are equal in length.

Therefore, side a = side b = side c = side d = 2 cm

Conclusion

Knowing the perimeter of all the geometrical shapes is a convenient way to ease various calculations. In this case, calculating the perimeter of a square can help one simplify multiple mathematical concepts. The above explanation deals with the definition, analysis, derivation, and examples of the perimeter of a square. The properties of a square help to calculate the area, perimeter, and length of its sides.

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