Worksheet on Area and Perimeter of Squares contains different questions related to the square that helps the students to prepare for the exam. We have covered each and every model related to the square area, perimeter, and diagonal on this page. You can also get the step by step process to solve the Area and Perimeter Word Problems. Practice all the questions without fail and verify your answers from here.

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1. Find the perimeter and area of the following squares whose dimensions are:

(a) 8 m

(b) 6.8 cm

(c) 12 m

## Solution:

(a)

Given that,

Square side length s = 8 m

Square perimeter p = 4s

p = 4 x 8 = 32 m

Square area A = s²

A = 8² = 8 x 8

A = 64 m²

∴ Square area is 64 m², perimeter is 32 m.

(b)

Given that,

Square side length s = 6.8 cm

Square perimeter p = 4s

p = 4 x 6.8

p = 27.2 cm

Square area A = s²

A = 6.8² = 6.8 x 6.8

A = 46.24 cm²

∴ The Square area is 46.24 cm², perimeter is 27.2 cm.

(c)

Given that,

Square side length s = 12 m

Square perimeter p = 4s

p = 4 x 12 = 48 m

Square area A = s²

A = 12²

A = 12 x 12 = 144 m²

∴ The Square area is 144 m², perimeter is 48 m.

2. Each side of a square is 2.6 cm. Find its perimeter, area?

## Solution:

Given that,

Square side = 2.6 cm

Square perimeter = 4 x side length

P = 4 x 2.6

P = 10.4 cm

Square area = side²

= 2.6² = 2.6 x 2.6

= 6.76 cm²

∴ Square perimeter is 10.4 cm, area is 6.76 cm².

3. Find the perimeter of a square whose area is 120 m².

## Solution:

Given that,

Square area A = 120 m²

Area A = Side²

120 = Side²

Side = √120

Side = 10.95

Square Perimeter P = 4side

P = 4 x 10.95

P = 43.817 m

∴ The perimeter of the square is 43.817 m.

4. Find the area of the square field whose perimeter is 240 m.

## Solution:

The perimeter of the square p = 240 m

p = 4 x side

side = p / 4

side = 240 / 4

side = 60

Area of the square = side²

A = 60²

A = 60 x 60 = 3600

∴ Area of the square is 3600 m².

5. A rope of length of 104 m is used to fence a square garden. What is the length of the side of the garden?

## Solution:

Given that,

The perimeter of the garden P = 104 m

We know that perimeter of a square = 4 × length of a side

So, 4 × length of a side = 104

The length of a side = 104/4

Side length = 26 m

∴ The length of the side of the garden is 26 m.

6. Lila has 16 square stamps of side 4 cm each. She glues them onto an envelope to form a bigger square. What area of the envelope does the bigger square cover?

## Solution:

16 square-shaped stamps can be arranged as 4 in each row. So it forms 4 rows and 4 columns.

Side of the formed square s = 4 + 4 + 4 + 4

s = 16 cm

Area of the formed square A = 16 x 16

= 256

∴ The area of the bigger square is 256 cm².

7. If the diagonal length of a square is 7 cm, find the square area, perimeter?

## Solution:

Given that,

The diagonal length of a square d = 7 cm

We know that, when you draw a diagonal in the square, it forms a right-angled triangle.

By using the Pythagorean theorem,

side² + side² = diagonal²

2side² = 7²

2side² = 49

side² = 49/2

side² = 24.5

side = √24.5

= 4.94 cm

The square perimeter p = 4 x side

p = 4 x 4.94

= 19.79 cm

The square area A = side²

A = 4.94² = 4.94 x 4.94

A = 24.4034 cm²

∴ The square area is 24.4034 cm², side length is 4.94 cm, and perimeter is 19.79 cm.

8. The diagonals of two squares are in the ratio 2:5. Find the ratio of their areas.

## Solution:

Let us take the diagonals of two squares as 2x, 5x

Area of the square formula when diagonal is given,

A = (1/2) x d²

Area of the first square = (1/2) x (2x)²

= (1/2)(4x²)

= 2x²

Area of the second square = (1/2) x (5x)²

= (1/2) x (25x²)

= 12.5x²

The ratio of their areas = 2x² : 12.5x²

= 4 : 25

So, the ratio of the two squares is 4 : 25.

9. The areas of a square and rectangle are equal. If the side of the square is 15 cm and the breadth of the rectangle 10 cm, find the length of the rectangle and its perimeter.

## Solution:

Given that,

Side of the square s = 15 cm

The breadth of the rectangle b = 10 cm

The areas of a square and rectangle are equal

Area of square = Area of Rectangle

s² = l x b

15² = l x 10

225 = l x 10

l = 225/10

l = 22.5

The perimeter of the rectangle p = 2(l + b)

= 2(22.5 + 10)

= 2(32.5) = 65

The perimeter of a square = 4 x side

= 4 x 15 = 60 cm

∴ The square, rectangle area is 225 cm², square perimeter is 60 cm, rectangle perimeter is 65 cm.

10. A wire is in the shape of a rectangle whose width is 12 cm is bent to form a square of side 17 cm. Find the rectangle length and also find which shape encloses more area.

## Solution:

Given that,

Rectangle width w = 12 cm

Square side = 17 cm

The perimeter of a rectangle = Perimeter of a square

2(l + w) = 4side

2(l + 12) = 4 x 17

2l + 24 = 68

2l = 68 – 24

2l = 44

l = 44/2

l = 22

Area of square = side²

= 17² = 17 x 17

= 289

Area of the rectangle = l x b

= 22 x 12 = 264

∴ Rectangle length is 22 cm, and square has more area.

11. The area of a square field is 49 hectares. Find the cost of fencing the field with a wire at the rate of $5 per m.

## Solution:

Given that,

Area of the square field = 49 hectares

1 hectare = 10000 sq.m.

So, 49 hectares = 49 x 10,000 = 4,90,000

So, the area of the square field = 4,90,000

Square area = side²

4,90,000 = side²

side = √(4,90,000)

side = 700

The perimeter of the square = 4 x side

P = 4 x 700 = 2800

Cost of fencing 1 m = $5

Cost of fencing 2800 m = 2800 x 5 = 14000

Hence The cost of fencing the square field is $14000.

12. How many square tiles of side 6 cm will be needed to fit in a square floor of a bathroom of side 600 cm. Find the cost of tiling at the rate of $65 per tile.

## Solution:

Given that,

Side length of a tile = 6 cm

Side length of bathroom = 600 cm

Area of the square = 600 x 600 = 360000

Area of the tile = 6 x 6 = 36

Number of tiles = Area of the square / Area of the tile

= 360000 / 36 = 10000

Cost of 1 tile = $65

Cost of tiling = 65 x 10000 = 650000

∴ Number of square tiles required is 10000, cost of tiles is $650000.

13. If it costs $420 to fence a square field at the rate of $4 per m, find the length of the side and the area of the field.

## Solution:

Given that,

The total cost of fencing = $420

The cost of fencing per m = $4

So, the Perimeter of the square field = 420/4

P = 105

Length of square = 105 / 4

Side = 26.25

Area of the square A = side²

A = (26.25)²

A = 26.25 x 26.25 = 689.0625

∴ The area of the field is 689.0625 m², side length is 26.25 m.