CBSE Class 6 Maths Chapter 6: Perimeter and Area – Important Questions with Answers (Free PDF Download)

1. What is the cost of tiling a rectangular plot of land 500 m long and 200 m wide at the rate of ₹8 per hundred sq m? 

Ans: Given:

Length of the plot $ l = 500 \, \text{m} $

Width of the plot $ w = 200 \, \text{m} $

Rate of tiling $ \text{₹} 8 $ per 100 square meters.

Formula:

The area of the plot is:

\[A = l \times w\]

Total cost of tiling is:

\[\text{Cost} = \left( \frac{A}{100} \right) \times \text{Rate per 100 sq m}\]

Calculate the area of the plot:

\[A = 500 \times 200 = 100,000 \, \text{sq m}\]

Now calculate the cost:

\[\text{Cost} = \left( \frac{100,000}{100} \right) \times 8 = 1000 \times 8 = \text{₹} 8000\]

The cost of tiling the plot is ₹ 8000.

2. Give the dimensions of a rectangle whose area is the sum of the areas of these two rectangles having measurements: 5 m × 10 m and 2 m × 7 m. 

Ans: Area of the first rectangle:

\[A_1 = 5 \times 10 = 50 \, \text{sq m}\]

Area of the second rectangle:

\[A_2 = 2 \times 7 = 14 \, \text{sq m}\]

Total area:

\[\text{Total area} = A_1 + A_2 = 50 + 14 = 64 \, \text{sq m}\]

Assume the length of the new rectangle is 8 meters. Then, the width will be:

\[\text{Width} = \frac{64}{8} = 8 \, \text{m}\]

The dimensions of the rectangle are 8 m × 8 m.

3. Shape A has an area of 18 square units and Shape B has an area of 20 square units. Shape A has a longer perimeter than Shape B. Draw two such shapes satisfying the given conditions. 

Ans:

4. A square piece of paper is folded in half. The square is then cut into two rectangles along the fold. Regardless of the size of the square, one of the following statements is always true. Which statement is true here? 

a. The area of each rectangle is larger than the area of the square. 

b. The perimeter of the square is greater than the perimeters of both the rectangles added together. 

c. The perimeters of both the rectangles added together is always $1\frac{1}{2}$  times the perimeter of the square. 

d. The area of the square is always three times as large as the areas of both rectangles added together. 

Ans: c.  The perimeters of both the rectangles added together is always $1\frac{1}{2}$  times the perimeter of the square.

5. A rectangle having sidelengths 5 cm and 3 cm is made using a piece of wire. If the wire is straightened and then bent to form a square, what will be the length of a side of the square? 

Ans: To solve this problem:

1. Find the perimeter of the rectangle:

The formula for the perimeter of a rectangle is:

\[     \text{Perimeter} = 2 \times (\text{length} + \text{breadth})     \]

For the given rectangle with side lengths of 5 cm and 3 cm:

\[     \text{Perimeter} = 2 \times (5 + 3) = 2 \times 8 = 16 \, \text{cm}  \]

So, the total length of the wire is 16 cm.

2. When the wire is bent to form a square, the perimeter of the square will also be 16 cm.

3. Find the side length of the square:

The formula for the perimeter of a square is:

\[     \text{Perimeter} = 4 \times \text{side}  \]

Given that the perimeter is 16 cm:

\[ 16 = 4 \times \text{side}     \]

Solving for side:

\[     \text{side} = 16 \div 4 = 4 \, \text{cm}  \]

Therefore, the length of each side of the square will be 4 cm.

6. The area of a rectangular garden 25 m long is 300 sq m. What is the width of the garden? 

Ans: Given:

Length of the garden $ l = 25 \, \text{m} $

Area of the garden $ A = 300 \, \text{sq m} $

Formula:

\[A = l \times w\]

Where:

A is the area,

l is the length,

w is the width.

 \[300 = 25 \times w\]

Divide both sides by 25:

\[w = \frac{300}{25} = 12 \, \text{m}\]

The width of the garden is 12 meters.

Extra Questions For Better Score

1. A square sheet of metal is cut into four equal smaller squares. Which of the following statements is always true?

a. The area of each smaller square is four times the area of the original square.
b. The perimeter of each smaller square is the same as the perimeter of the original square.
c. The total perimeter of all four smaller squares is twice the perimeter of the original square.
d. The area of the original square is smaller than the sum of the areas of the four smaller squares.

Solution: c. The total perimeter of all four smaller squares is twice the perimeter of the original square.

2. A wire of length 24 cm is bent into the shape of a rectangle with one side measuring 8 cm. What is the length of the other side?

Solution:

1. The formula for the perimeter of a rectangle is:
   Perimeter = 2 × (length + width)

2. Given perimeter = 24 cm and length = 8 cm:
   24 = 2 × (8 + w)
   12 = 8 + w
   w = 4 cm

The width of the rectangle is 4 cm.

3. A rectangular field has an area of 540 sq. meters and a length of 30 meters. What is the width of the field?

Solution: Using the area formula:

A = l × w

540 = 30 × w

Dividing both sides by 30:

w = $\dfrac{540}{30}$= 

w ​= 18m

The width of the field is 18 meters.

4. A rectangular plot of land has a perimeter of 64 m. If the length is 20 m, what is the width?

Solution: Using the perimeter formula:

Perimeter = 2 × (length+width)

64 = 2 × (20 + w)

32 = 20 + w

w = 12m

The width of the plot is 12 meters.

5. A wire of length 20 cm is used to make a square. What is the length of each side of the square?

Solution: Using the perimeter formula of a square:

Perimeter = 4 × side

Given perimeter = 20 cm:

20 = 4 × side

side = 20 ÷ 4

side = 5 cm

The length of each side of the square is 5 cm.

This page has a set of important questions on CBSE Class 6 Maths Chapter 6 Perimeter and Area. It includes a variety of extra questions and short question answers to help with exam preparation. 

The questions on this page are carefully selected from previous test papers and solved by Vedantu experts to improve understanding in solving problems. 

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