Square is a two-dimensional figure characterized by four sides, preferably, denoted as edges and its intersection points known as the vertices respectively. All four sides of the square are equal in length. It is a special case of a rectangle where all the sides are equalÂ

**Properties of a square**

Some of the properties of a square are as follows :Â

- All four sides of the square are equal to each other.
- The opposite sides of a square are parallel to each other.
- All angles of the square measure 90Â°.
- The sum of all interior angles is 360Â°.
- Length of diagonals is equal.
- The length of the diagonal with sides s is âˆš2 Ã— s
- Since the sides of a square are parallel, it is also called a parallelogram.

**Perimeter of a square**

Perimeter of a square = Sum of all four sides

Therefore,

Let us assume the side of the square to be x.

Now,

Since all the four sides of the square are equal in length, we have,

Perimeter of a square = x + x + x + x

= 4x

### What is the perimeter of a 2 inch square if the length of each side is doubled?

**Solution:**

Originally, we have,

Side of a square, s = 2 inch

Perimeter of the square, P = 4 * side of the square

= 4 * s inch

= 4 * 2 inch

= 8 inch

Thus, P = 8 inches

Now, we have,

Side of the square is doubled.

Therefore,

Side of a square, s’ = 2 * 2 inch

= 4 inch

Perimeter of the square, P’ = 4 * side of the square

= 4 * s’ inch

= 4 * 4 inch

= 16 inch

P’ = 16 inches

Thus, the perimeter becomes two times, when each side is doubled.

### Sample Questions

**Question 1. Assume that the side of a square is 40 inches if the sides of the square are tripled, Then calculate how many times the new perimeter of the square becomes?**

**Solution:**

Here we have to find how many times the perimeter will be increased if the side of the square is tripled

As we know that

Perimeter of a square = 4 Ã— side

Given: Side of the square is 40 inch

Perimeter of a square = 4 Ã— 40

Perimeter of a square = 160 inch

Further,

When the side of the square is tripled

Side of the new square = 3 Ã— 40

Side of the new square = 120 inch

Now,

Perimeter of the new square = 4 Ã— side

Perimeter of the new square = 4 Ã— 120

Perimeter of the new square = 480 inch

Further,Â

To find how many times the perimeter is increased

Increase in the perimeter =Â

Increase in the perimeter =Â

Increase in the perimeter = 3 times

Therefore,

We can see that the perimeter of the new square is triple the perimeter of the original square

Thus,

The perimeter of a square is increased by 3 times when its sides are tripled.

**QuestionÂ 2. Calculate how many times the perimeter of a square will be reduced if the side of a square is reduced to half. Given that the side of the original square is 25 inches?**

**Solution:**

Here we have to find how many times the perimeter will be reduced if the side of the square is halved.

As we know that

Perimeter of a square = 4 Ã— side

Given: Side of the square is 25 inch

Perimeter of a square = 4 Ã— 25

Perimeter of a square = 100 inch

Further,

When the side of the square is halved

Side of the new square =Â

Side of the new square = 12.5 inch

Now,

Perimeter of the new square = 4 Ã— side

Perimeter of the new square = 4 Ã— 12.5

Perimeter of the new square = 50 inch

To find how many times the perimeter is decreased

Decrease in the perimeter =Â

Decrease in the perimeter =Â

Decrease in the perimeter = 2 times

Therefore,

We can see that the perimeter of the new square is reduced by 2 times the perimeter of the original square

Thus,

The perimeter of a square is reduced to half when its sides are halved.

**QuestionÂ 3. Assume that the perimeter of a square is increased by four times, So find how many times the new side of the square becomes. It is given that the perimeter of the original square is 120 feet?**

**Solution:**

Here we have to find the increase in the side of the square when its perimeter is increased by four times

As we know that

Perimeter of a square = 4 Ã— side

Given: Perimeter of the original square is 120 feet

Perimeter of the original square = 120 feet

Perimeter of the original square = 4 Ã— side

120 = 4 Ã— side

Side =Â

Side of the original square = 30 feet

Further,

Perimeter of the original square is increased by four times

Perimeter of the new square = 4 Ã— 120

Perimeter of the new square = 480 feet

Perimeter of the new square = 4 Ã— side

480 = 4 Ã— side

Side =Â

Side = 120 feet

Side of the new square = 120 feet

Now,

Side of the original square = 30 feet

Side of the new square = 120 feet

To find how many times the side is increased

Increase in the side =Â

Increase in the perimeter =Â

Increase in the perimeter = 4 times

Therefore,

We can see that the side of the new square is increased by four times the side of the original square

Thus,

The side of a square is increased by four times when its perimeter is increased by four times.

**QuestionÂ 4. Calculate the perimeter of the square if the****area of the square is 64 inch**^{2}**?**

**Solution:**

Here we have to find the perimeter of the square by the given area.

Given: Area of the square is 64 inch

^{2}.As we know that

Area of the square = Side Ã— Side

Area of the square = s Ã— s

64 = s Ã— s

s

^{2}= 64s =Â

s = 8 inch

Side of the square is 8 inch

Further,

Perimeter of the square = 4 Ã— side

Perimeter of the square = 4 Ã— 8

Perimeter of the square = 32 inch

Therefore,

Perimeter of the square is 32 inch.

**QuestionÂ 5. Assume that the side of a square is increased by 8 times, so****calculate by how many times the area of the new square will become. Given that the side of the original square is 20 inches.**

**Solution:**

Here we have to find how many times the area will be increased if the side of the square is increased by 8 times.

As we know that

Area of a square = side Ã— side

Given: Side of the square is 20 inch

Area of a square = 20 Ã— 20

Area of a square = 400 inch

^{2}Further,

When the side of the square is increased by 8 times

Side of the new square = 8 Ã— 20

Side of the new square = 160 inch

Now,

Area of the new square = side Ã— side

Area of the new square = 160 Ã— 160

Perimeter of the new square = 25600 inch

^{2}Further,

To find how many times the area is increased

Increase in the area =Â

Increase in the area =Â

Increase in the area = 64 times

Therefore,

We can see that the area of the new square is 4 times the area of the original square

Thus,

The area of a square is increased by 64 times when its sides are increased by 8 times.