Maths Class 6 Important Questions Chapter 6 Ganita Prakash

Perimeter and Area

1. What is the perimeter of a rectangle with a length of 12 cm and a breadth of 8 cm?

Solution:

• Perimeter of a rectangle = 2 × (length + breadth)
• Perimeter = 2 × (12 cm + 8 cm) = 2 × 20 cm = 40 cm.

2. Find the perimeter of a square whose side length is 5 m.

Solution:

• Perimeter of a square = 4 × length of a side
• Perimeter = 4 × 5 m = 20 m.

3. A triangle has sides of length 4 cm, 5 cm, and 7 cm. What is its perimeter?

Solution:

• Perimeter of a triangle = sum of all sides
• Perimeter = 4 cm + 5 cm + 7 cm = 16 cm.

4. A rectangular tablecloth is 3 m long and 2 m wide. How much lace is needed to go around its edges?

Solution:

• Perimeter of a rectangle = 2 × (length + breadth)
• Perimeter = 2 × (3 m + 2 m) = 2 × 5 m = 10 m.

5. A square park has sides of length 75 m. Usha walks 3 rounds around the park. What is the total distance she walks?

Solution:

• Perimeter of the square = 4 × length of a side
• Perimeter = 4 × 75 m = 300 m.
• Distance covered in 3 rounds = 3 × 300 m = 900 m.

6. A piece of wire is 36 cm long. If it is bent to form a square, what will be the length of each side?

Solution:

• Perimeter of a square = 4 × length of one side
• Total length of wire = 36 cm.
• Length of one side = 36 cm ÷ 4 = 9 cm.

7. A rectangular park has a length of 150 m and a breadth of 120 m. What is the total cost to fence it if the cost of fencing is ₹40 per meter?

Solution:

• Perimeter of the rectangle = 2 × (length + breadth)
• Perimeter = 2 × (150 m + 120 m) = 2 × 270 m = 540 m.
• Cost = 540 m × ₹40/m = ₹21,600.

8. What is the perimeter of a rectangle whose length is 14 cm and breadth is 7 cm?

Solution:

• Perimeter of a rectangle = 2 × (length + breadth)
• Perimeter = 2 × (14 cm + 7 cm) = 2 × 21 cm = 42 cm.

9. A square has a perimeter of 20 cm. What is the length of one side?

Solution:

• Perimeter of a square = 4 × length of one side
• Let the length of one side = x.
• 4 × x = 20 cm.
• x = 20 cm ÷ 4 = 5 cm.

10. The perimeter of a triangle is 55 cm. If two sides are 20 cm and 14 cm, what is the length of the third side?

Solution:

• Perimeter of a triangle = sum of all sides.
• 55 cm = 20 cm + 14 cm + third side.
• Third side = 55 cm – (20 cm + 14 cm) = 55 cm – 34 cm = 21 cm.

11. A square garden has a side of 12 m. What is its perimeter and area?

Solution:

• Perimeter of the square = 4 × length of a side
• Perimeter = 4 × 12 m = 48 m.
• Area of the square = side × side = 12 m × 12 m = 144 sq m.

12. Find the width of a rectangular garden if the perimeter is 60 m and the length is 20 m.

Solution:

• Perimeter of a rectangle = 2 × (length + breadth).
• 60 m = 2 × (20 m + breadth).
• 60 m = 40 m + 2 × breadth.
• 2 × breadth = 60 m – 40 m = 20 m.
• Breadth = 20 m ÷ 2 = 10 m.

13. A rectangular field has a length of 50 m and a breadth of 30 m. If a path 2 m wide is built around the field, what is the area of the path?

Solution:

• Outer rectangle (with the path) length = 50 m + 2 × 2 m = 54 m.
• Outer rectangle (with the path) breadth = 30 m + 2 × 2 m = 34 m.
• Area of the outer rectangle = 54 m × 34 m = 1836 sq m.
• Area of the original field = 50 m × 30 m = 1500 sq m.
• Area of the path = 1836 sq m – 1500 sq m = 336 sq m.

14. A wire is bent to form a rectangle with a length of 12 cm and a breadth of 6 cm. If the same wire is bent to form a square, what will be the length of each side of the square?

Solution:

• Perimeter of the rectangle = 2 × (length + breadth) = 2 × (12 cm + 6 cm) = 2 × 18 cm = 36 cm.
• Perimeter of the square = 4 × length of one side.
• Length of one side = 36 cm ÷ 4 = 9 cm.

15. A farmer has a rectangular field with a length of 230 m and a breadth of 160 m. If he wants to put 3 rounds of fencing around the field, what is the total length of fencing required?

Solution:

• Perimeter of the field = 2 × (length + breadth) = 2 × (230 m + 160 m) = 2 × 390 m = 780 m.
• Total length of fencing for 3 rounds = 3 × 780 m = 2340 m.