CBSE Important Questions for Class 6 Maths Perimeter and Area - 2025-26
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:
The formula for the perimeter of a rectangle is:
Perimeter = 2 × (length + width)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.
Important Study Materials for Class 6 Maths Chapter 6 Perimeter and Area
CBSE Class 6 Maths Chapter-wise Important Questions
Important Related Links for CBSE Class 6 Maths
FAQs on CBSE Important Questions for Class 6 Maths Perimeter and Area - 2025-26
1. What are some frequently asked 1-mark questions from CBSE Class 6 Maths Chapter 6, Perimeter and Area?
For the 2025-26 exams, important 1-mark questions typically focus on direct formula application. You can expect questions like:
- Finding the perimeter of a regular shape like a square or an equilateral triangle given one side.
- Calculating the area of a square or rectangle with given dimensions.
- Questions asking for the formula for the perimeter of a regular pentagon or hexagon.
- Finding a missing side of a rectangle when the perimeter and one side are provided.
2. Which type of long-answer questions (3-mark) are expected from the Perimeter and Area chapter?
Important long-answer questions often involve multiple steps and real-world applications. Key types include:
- Calculating the cost of fencing a rectangular park, where you first find the perimeter and then multiply by the cost per metre.
- Finding the cost of tiling or carpeting a room, which requires calculating the area first.
- Problems where you need to compare the perimeter or area of two different shapes (e.g., a square and a rectangle).
- Word problems that require you to find the number of tiles needed to cover a floor.
3. Are there any important questions that combine the concepts of both perimeter and area?
Yes, a classic important question type combines both concepts. For example, a problem might state: 'A wire is in the shape of a rectangle of length 10 cm and breadth 6 cm. If the same wire is rebent into a square, what will be the measure of its side? Also, find which shape encloses more area.' This type of question tests your understanding that the perimeter (length of the wire) remains constant.
4. How does practising important questions for Class 6 Maths Chapter 6 help in scoring well in exams?
Practising a curated list of important questions helps in several ways. It familiarises you with the exam pattern and the types of problems frequently asked. It improves your problem-solving speed and accuracy, which is crucial for time management. Most importantly, it helps you identify conceptual weak points and application-based scenarios, ensuring you are well-prepared for the final exam.
5. What is the main difference between perimeter and area, and what is a common mistake to avoid in exams?
The main difference is what they measure:
- Perimeter is the total length of the boundary of a closed figure. It is a one-dimensional measure (units: cm, m).
- Area is the total surface covered by a closed figure. It is a two-dimensional measure (units: sq. cm, sq. m).
A common mistake is confusing the units. Always write 'cm' or 'm' for perimeter and 'sq. cm' or 'sq. m' for area. Using the wrong unit can lead to a loss of marks.
6. How do we solve important questions about finding the area of a path built around a rectangular field?
This is a higher-order thinking skill (HOTS) question. The standard approach involves these steps:
- Calculate the dimensions of the outer rectangle (field + path).
- Calculate the area of this outer rectangle.
- Calculate the area of the inner rectangle (the field itself).
- Subtract the area of the inner rectangle from the area of the outer rectangle. The result is the area of the path.
7. Why is it important to use the correct units (like cm, m, sq. cm, sq. m) when solving problems on Perimeter and Area?
Using the correct units is critical because they define what you are measuring. A perimeter of '10 cm' means a length, while an area of '10 sq. cm' means a surface space. In exams, providing an answer without the correct unit or with the wrong one (e.g., writing 'cm' for area) is considered a conceptual error and will likely result in a deduction of marks. It shows a lack of understanding of the fundamental concepts.
