## 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.

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