Perimeter of Square Questions

Perimeter of square questions is provided here with detailed solutions for students to practice. In mensuration, the perimeter of a shape refers to the length of the boundary of the given shape; for a regular geometrical shape, we have definite formulas to calculate the perimeter of respective shapes. The perimeter of a square is given by the formula, 4 × sides. Since the length of each side of a square is equal,

Check out more formulas for the perimeter of different shapes.

Perimeter is a physical quantity which ultimately represents a length; hence its unit is also the same as that of the unit of length. Students from grades 1 to 7 can solve the questions provided here. One must practice these questions to get a thorough knowledge of the concept of perimeter and excel in their examinations.

Perimeter of Square Questions with Solutions

Let us solve some questions related to the perimeter of the square given below.

Question 1: Find the perimeter of a square whose length of each side is 8 cm.

Solution:

Side of square = 8 cm

Perimeter of square = 4 × side

= 4 × 8 = 32 cm.

Thus, the perimeter of the square is 32 cm.

Question 2: Find the perimeter of a square whose length of each side is 2½ metres.

Solution:

Side of square = 2½ m = 5/2 m

Perimeter of square = 4 × side

= 4 × 5/2 = 20/2 = 10 m.

Thus, the perimeter of the square is 10 m.

Question 3: Find the length of the sides of the square park, whose perimeter is 232 m.

Solution:

Perimeter of square park = 4 × side = 232 m

⇒ side = 232/4

⇒ side = 58 m.

Therefore, the length of the sides of the square park is 58 m.

Also, read

• Perimeter of Square
• Perimeter of Rectangle
• Perimeter of Triangle
• Circumference of Circle

Question 4: Find the length of the sides of a square field whose boundary length is 558.2 metres.

Solution:

The boundary length of a square field = perimeter of the square field

∴ 4 × side = 558.2

⇒ side = 558.2/4

⇒ side = 139.55 m

Therefore, the length of the sides of the square field is 139.55 m.

Question 5: The cost of fencing wire per metre is ₹ 45. Suppose a square park with a side of 75 m has to be fenced 4 rounds. What will be the cost of fencing wire for this?

Solution:

Side of the square park = 75 m

Perimeter of square park = 4 × 75 = 300 m

Cost of per meter wire = ₹ 45

Cost of 300 m wire = 300 × 45 = ₹ 13,500

Cost of fencing 4 rounds = 13,500 × 4 = ₹ 54,000

Therefore, the total cost of fencing is ₹ 54,000.

Question 6: The length of the diagonal of a square is 32√2 cm. Find the perimeter of the square.

Solution:

Length of diagonal = 32√2 cm

Perimeter of square = 2√2 × 32√2 cm

= 2 × 2 × 32 (∵ √2 × √2 = 2)

= 128 cm

Question 7: Find the length of diagonals of a square whose perimeter is 240 cm.

Solution:

Perimeter of square = 2√2 × diagonal = 240 cm

⇒ diagonal = 240/2√2 = 60√2 cm

Therefore, the diagonal of the square is 60√2 cm.

Question 8: Sides of two squares are in the ratio of 2:5. Find the ratio of their perimeter.

Solution:

Let the sides of two squares be 2x and 5x

Perimeter of the first square = 4 × 2x = 8x

Perimeter of the second square = 4 × 5x = 20x

Ratio of the perimeters = 8x/20x = ⅖ = 2:5.

Therefore, their perimeter is also in the ratio 2:5.

Question 9: Nine small squares of perimeter 8 cm are joined together to form a big square. Find the perimeter of the bigger square.

Solution:

Perimeter of each small square = 8 cm

Side length of each small square = 8/4 = 2 cm.

Nine small squares are arranged to form a big square, so they must be arranged in the form of 3 × 3 squares.

The side length of the bigger square = 3 × 2 = 6 cm

Perimeter of the bigger square = 4 × 6 = 24 cm.

Question 10: The perimeter of two square frames is 56 cm and 90 cm, respectively. Suppose there is another square frame whose perimeter is twice the sum of the perimeters of the previous two square frames. Find the side length and perimeter of the bigger square frame.

Solution:

Perimeter of the square whose side length is 56 cm = 4 × 56 = 224 cm

Perimeter of the square whose side length is 90 cm = 4 × 90 = 360 cm

Perimeter of the bigger square = 2 × (224 + 360)

= 2 × 584 = 1168 cm

But, 4 × side = 1168 cm

⇒ side = 1168/4

⇒ side = 292 cm

Thus, side length and perimeter of the bigger square frame is 292 cm and 1168 cm, respectively.

Question 11: A wire is bent into a rectangle whose length is 20 cm, and breadth is half the length. The same wire is rebent into a square. Find the side length of the square so formed.

Solution:

Length of the rectangle = 20 cm

Breadth of the rectangle = 20/2 = 10 cm

Perimeter of the rectangle = 2 × (length + breadth)

= 2 × ( 20 + 10) = 2 × 30

= 60 cm.

Now, since the same wire is used to make the square, then

the length of the wire = perimeter of the rectangle = perimeter of the square

∴ Perimeter of square = 60 cm

⇒ 4 × sides = 60

⇒ sides = 60/4

⇒ sides = 15 cm

Question 12: A square is inscribed in a circle of radius 7 cm such that the diameter of the circle is equal to the diagonal of the square. Find the perimeter of the square. (Use √2 = 1.414)

Solution:

Radius of the circle = 7 cm

Diameter of the circle = 2 × 7 = 14 cm

Diagonal of square = 14 cm

Perimeter of square = 2√2 × 14

= 2 × 1.414 × 14

= 39.592 cm.

Video Lesson on Perimeter of Shapes

Practice Questions on Perimeter of Square

1. Find the perimeter of a square whose sides are of length 28 cm.

2. Find the perimeter of a square whose diagonals are of length 15√2 cm.

3. Find the perimeter of a square whose sides are equal to the radius of the circle with a circumference of 132 cm.

4. Find the cost of fencing a square land whose side length is 125 m, if the cost of fencing per 10 m is ₹ 450.

5. A wire is bent into a circle whose radius is 25 cm. The same wire is rebent into a square. Find the side length of the square so formed.

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