✅ Formula for calculating the perimeter of a square ⭐️⭐️⭐️⭐️⭐

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Perimeter of Square

The perimeter of a square is defined as the total length that its boundary covers. The perimeter of any closed geometrical object is calculated by finding the distance around that object. For a square, the perimeter can be calculated by finding the sum of all the sides. Let us have a look at the article in order to understand the concept in a better way.

What is the Perimeter of Square?

A perimeter of any shape is either a path that encompasses/surrounds/outlines a shape (in two dimensions) or its length (one-dimensional). The perimeter of a square can be calculated by adding the length of all its sides.

Perimeter of Square Formula

The formula to calculate the perimeter of a square is as, mathematically expressed as;
Perimeter of square, (P) = 4 × Side

Example: Calculate the perimeter of a square with each side measuring 7 units.

Solution: Given: Side length of square = 7 units
We know, using the perimeter of a square formula,

Perimeter of square = 4 × Side
⇒ 4 × 7 = 28 units

Derivation of Perimeter of Square Formula

The perimeter of the square is defined as the total length of the boundary of a square. In order to calculate the perimeter of the square, we will find the sum of all of its sides. Since, all the sides of a square are equal, for a square, with each side measuring “s” units, perimeter will thus be given as,

Perimeter of square = s + s + s + s
⇒ Perimeter of square = 4s, where “s” is the side length of the square.

How to Calculate Perimeter of a Square?

The perimeter of the square can be calculated following different methods depending upon the known parameters. This section will cover the method using,

  • Side length
  • Diagonal
  • Area

Perimeter of Square Using Side Length

We generally find the perimeter for this case by multiplication of side length with 4.To find the perimeter of a square using the side length, we can follow the steps given below,

  • Step 1: Note down the measurement of the side.
  • Step 2: Multiply the noted length with 4.
  • Step 3: Express the obtained result with the unit.

Perimeter of Square Using Diagonal

The perimeter of the square can also be calculated if the length of its diagonal is known to us. To find the perimeter of a square using the diagonal, we can follow the steps given below,

  • Step 1: Note down the measurement of the diagonal of the square.
  • Step 2: Calculate the side length using the diagonal,
    Side = diagonal/√2 = √2 × diagonal/ 2
  • Step 3: Multiply this obtained value of side length, (√2 × diagonal/ 2) by 4 and express the answer in units,
    Perimeter = (√2 × diagonal/2) × 4 = 2√2 × diagonal units.

Perimeter of Square Using Area of Square

We can find the perimeter of the square given the area. To find the perimeter of a square using the area, we can follow the steps given below,

  • Step 1: Note down the area of square.
  • Step 2: Calculate the side length using the area,
    Side = √area
  • Step 3: Multiply this obtained value of side length, (√area) by 4 and express the answer in units,
    Perimeter = (√area) × 4 = 4√area units.

Let us have a look at a few solved examples to understand the perimeter of the square better.

Tricky math problems with the squares:

Type I: Finding side length when only the perimeter is given.

Example 1. If the perimeter of the given square is 12 cm. What will be the length of its side?

Solution: Given, the perimeter of the square is 12 cm.

Let the side length be ‘a’ cm.

We know that, the perimeter of a square = 4 × (side length)

12=4×(a)

a = 3 cm

Type II: Finding sides using square properties.

Example 2.If a = 4 cm in the given square. Find b, c. and d.

Solution: Given that side a = 4 cm.

To find side b, c, and d  we use the property of the square which states that all the sides of a square are equal.

Therefore, a = b = c = d = 4 cm

Type III: Finding perimeter when one of the sides is given.

Example 3. One of the sides of a square is 5 cm. What will be its perimeter?

Solution: Given, one side of the square is 5 cm.

We know that, the perimeter of a square = 4 × (side length)

= 4×(5)

= 20 cm

Example 4. The length of a side of the square wooden frame is 5 cm. Find the total length of the wood used in the frame.

Solution: Given, the length of a side of this wooden frame is 5 cm.

As we know, the perimeter of a square = 4× (side length)

= 4  (5)

= 20 cm

Hence, the total length of the wood used is 20 cm.

  Fun FactsSquares are one of the three most basic shapes on the earth. The other two are circles and triangles.

Properties of square:
·  Diagonals of a square (quadrangle) bisect each other
·  Diagonals of a square (quadrangle) bisect its angles.
·  Diagonals of a square (quadrangle) are perpendicular.
·  Opposite sides of a square (quadrangle) are both parallel and equal.
·  All four angles of a square (quadrangle) are equal. (Square is 360/4 = 90 degrees, so every angle of a square (quadrangle) is a right angle.)
·  The diagonals of a square (quadrangle) are equal.

Perimeter of Square Examples

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