Perimeter and Area — Class 6 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 6 Mathematics chapter "Perimeter and Area" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 6 Mathematics chapter "Perimeter and Area" — 8 important questions with detailed answers for CBSE board ex…
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NCERT Solutions for Class 6 Mathematics — Perimeter and Area. Step-by-step answers to all 8 textbook questions from this chapter, written for CBSE board preparation and free to use.
Perimeter and Area — All 8 Questions Solved
Q1. Find the perimeter of a rectangle with length 12 cm and breadth 8 cm.
Perimeter of rectangle = 2 × (length + breadth)
Step 1: Length = 12 cm, Breadth = 8 cm
Step 2: Perimeter = 2 × (12 + 8)
Step 3: Perimeter = 2 × 20
Step 4: Perimeter = 40 cm
Final Answer: 40 cm
Q2. A square has side 7 cm. Find its area and perimeter.
Area of square = side × side
Step 1: Side = 7 cm
Step 2: Area = 7 × 7 = 49 cm²
Perimeter of square = 4 × side
Step 3: Perimeter = 4 × 7 = 28 cm
Final Answer: Area = 49 cm², Perimeter = 28 cm
Q3. A rectangular field has length 50 m and breadth 30 m. Find the area of the field.
Area of rectangle = length × breadth
Step 1: Length = 50 m, Breadth = 30 m
Step 2: Area = 50 × 30
Step 3: Area = 1500 m²
Final Answer: 1500 m²
Q4. If the perimeter of a square is 36 cm, what is the length of its side?
Perimeter of square = 4 × side
Step 1: Perimeter = 36 cm
Step 2: 4 × side = 36
Step 3: side = 36 ÷ 4
Step 4: side = 9 cm
Final Answer: 9 cm
Q5. Find the area of a triangle with base 12 cm and height 8 cm.
Area of triangle = (1/2) × base × height
Step 1: Base = 12 cm, Height = 8 cm
Step 2: Area = (1/2) × 12 × 8
Step 3: Area = (1/2) × 96
Step 4: Area = 48 cm²
Final Answer: 48 cm²
Q6. A rectangle has area 120 cm² and length 15 cm. Find its breadth.
Area of rectangle = length × breadth
Step 1: Area = 120 cm², Length = 15 cm
Step 2: 15 × breadth = 120
Step 3: breadth = 120 ÷ 15
Step 4: breadth = 8 cm
Final Answer: 8 cm
Q7. Find the perimeter of a triangle with sides 5 cm, 7 cm, and 6 cm.
Perimeter of triangle = sum of all three sides
Step 1: Side 1 = 5 cm, Side 2 = 7 cm, Side 3 = 6 cm
Step 2: Perimeter = 5 + 7 + 6
Step 3: Perimeter = 18 cm
Final Answer: 18 cm
Q8. A square field has side 25 m. Find the cost of fencing it at ₹10 per metre.
Perimeter of square = 4 × side
Step 1: Side = 25 m
Step 2: Perimeter = 4 × 25 = 100 m
Step 3: Cost = Perimeter × rate per metre
Step 4: Cost = 100 × 10 = ₹1000
Final Answer: ₹1000
Perimeter and Area — Practice MCQs with Answers
Attempt these 20 multiple-choice questions after working through the solutions above. Each carries the correct option and the reasoning behind it, so a wrong answer tells you which idea to revisit.
MCQ 1. A square garden has a side of 10 meters. What is the perimeter of the garden?
- A. 10 m
- B. 20 m
- C. 30 m
- D. 40 m
Answer: D. 40 m — The perimeter of a square is calculated by adding the lengths of all four sides, or 4 × side. So, 4 × 10 m = 40 m.
MCQ 2. What is the area of a rectangular table with a length of 50 cm and a width of 30 cm?
- A. 80 cm²
- B. 150 cm²
- C. 1500 cm²
- D. 160 cm²
Answer: C. 1500 cm² — The area of a rectangle is found by multiplying its length by its width. So, 50 cm × 30 cm = 1500 cm².
MCQ 3. The perimeter of a rectangular park is 240 meters. If its length is 80 meters, what is its width?
- A. 40 m
- B. 60 m
- C. 80 m
- D. 160 m
Answer: A. 40 m — Perimeter of a rectangle = 2 × (length + width). So, 240 = 2 × (80 + width). This means 120 = 80 + width, so width = 120 - 80 = 40 m.
MCQ 4. A floor is 5 meters long and 4 meters wide. It is to be covered with square tiles of side 20 cm. How many tiles will be required?
- A. 500 tiles
- B. 1000 tiles
- C. 2500 tiles
- D. 50 tiles
Answer: A. 500 tiles — First, convert the floor dimensions to cm: 5 m = 500 cm, 4 m = 400 cm. Area of floor = 500 cm × 400 cm = 200,000 cm². Area of one tile = 20 cm × 20 cm = 400 cm². Number of tiles = Total area / Area of one tile = 200,000 / 400 = 500 tiles.
MCQ 5. A triangle has sides of length 7 cm, 9 cm, and 12 cm. What is its perimeter?
- A. 28 cm
- B. 21 cm
- C. 18 cm
- D. 20 cm
Answer: A. 28 cm — The perimeter of a triangle is the sum of the lengths of its three sides. So, 7 cm + 9 cm + 12 cm = 28 cm.
MCQ 6. The area of a square field is 100 square meters. What is the length of one side of the field?
- A. 10 m
- B. 25 m
- C. 50 m
- D. 100 m
Answer: A. 10 m — The area of a square is side × side. Since 10 × 10 = 100, the length of one side is 10 meters.
MCQ 7. Rohan wants to put a fence around his rectangular garden. The garden is 15 meters long and 10 meters wide. What is the total length of fencing required?
- A. 25 m
- B. 50 m
- C. 75 m
- D. 150 m
Answer: B. 50 m — The length of fencing required is equal to the perimeter of the garden. Perimeter of a rectangle = 2 × (length + width) = 2 × (15 m + 10 m) = 2 × 25 m = 50 m.
MCQ 8. Which of the following is a unit of area?
- A. centimeter
- B. meter
- C. square centimeter
- D. kilometer
Answer: C. square centimeter — Area is measured in square units, such as square centimeter (cm²), square meter (m²), etc.
MCQ 9. A rectangle has a length of 8 cm and a width of 5 cm. A square has a side of 6 cm. Which shape has a larger area?
- A. Rectangle
- B. Square
- C. Both have the same area
- D. Cannot be determined
Answer: A. Rectangle — Area of rectangle = length × width = 8 cm × 5 cm = 40 cm². Area of square = side × side = 6 cm × 6 cm = 36 cm². The rectangle has a larger area.
MCQ 10. A rectangular plot has a perimeter of 300 meters. If its width is 60 meters, what is its length?
- A. 90 m
- B. 120 m
- C. 150 m
- D. 180 m
Answer: A. 90 m — Perimeter of a rectangle = 2 × (length + width). So, 300 m = 2 × (length + 60 m). Dividing by 2, 150 m = length + 60 m. Therefore, length = 150 m - 60 m = 90 m.
MCQ 11. If each square in a grid represents 1 square centimeter, how would you find the area of an irregular shape drawn on the grid?
- A. By measuring its sides
- B. By using a ruler to draw a rectangle around it
- C. By counting the number of full and half squares it covers
- D. By using a protractor
Answer: C. By counting the number of full and half squares it covers — For irregular shapes on a grid, the area is estimated by counting the number of full squares completely inside the shape and adding half the number of squares that are more than half covered.
MCQ 12. A rectangular plot has a length of 20 m and a width of 15 m. If a square garden of side 5 m is made inside the plot, what is the area of the remaining plot?
- A. 225 m²
- B. 275 m²
- C. 300 m²
- D. 325 m²
Answer: B. 275 m² — Area of the rectangular plot = 20 m × 15 m = 300 m². Area of the square garden = 5 m × 5 m = 25 m². Area of the remaining plot = Area of rectangular plot - Area of square garden = 300 m² - 25 m² = 275 m².
MCQ 13. What does the perimeter of a shape represent?
- A. The space inside the shape
- B. The boundary of the shape
- C. The number of corners it has
- D. The volume it occupies
Answer: B. The boundary of the shape — The perimeter is the total length of the boundary or outline of a two-dimensional shape.
MCQ 14. A wire is bent to form a square with a perimeter of 36 cm. If the same wire is straightened and then bent to form an equilateral triangle, what will be the length of each side of the triangle?
- A. 9 cm
- B. 12 cm
- C. 18 cm
- D. 36 cm
Answer: B. 12 cm — The length of the wire is equal to the perimeter of the square, which is 36 cm. When this wire is bent into an equilateral triangle, its perimeter will also be 36 cm. Since an equilateral triangle has three equal sides, the length of each side will be 36 cm / 3 = 12 cm.
MCQ 15. Two different shapes, A and B, have the same perimeter. Shape A is a square with a side of 10 cm. Shape B is a rectangle with a length of 12 cm. What is the width of shape B?
- A. 6 cm
- B. 8 cm
- C. 10 cm
- D. 12 cm
Answer: B. 8 cm — Perimeter of square A = 4 × side = 4 × 10 cm = 40 cm. Since both shapes have the same perimeter, the perimeter of rectangle B is also 40 cm. Perimeter of rectangle B = 2 × (length + width). So, 40 cm = 2 × (12 cm + width). Dividing by 2, 20 cm = 12 cm + width. Therefore, width = 20 cm - 12 cm = 8 cm.
MCQ 16. What is the perimeter of a square with a side of 5 cm?
- A. 10 cm
- B. 20 cm
- C. 25 cm
- D. 15 cm
Answer: B. 20 cm — The perimeter of a square is 4 times its side. So, 4 * 5 cm = 20 cm.
MCQ 17. A rectangle has a length of 8 cm and a breadth of 3 cm. What is its perimeter?
- A. 11 cm
- B. 22 cm
- C. 24 cm
- D. 16 cm
Answer: B. 22 cm — The perimeter of a rectangle is 2 * (length + breadth). So, 2 * (8 + 3) cm = 2 * 11 cm = 22 cm.
MCQ 18. Find the area of a square whose side is 7 cm.
- A. 14 cm²
- B. 28 cm²
- C. 49 cm²
- D. 70 cm²
Answer: C. 49 cm² — The area of a square is side * side. So, 7 cm * 7 cm = 49 cm².
MCQ 19. A rectangular field is 10 m long and 6 m wide. What is its area?
- A. 16 m²
- B. 32 m²
- C. 60 m²
- D. 100 m²
Answer: C. 60 m² — The area of a rectangle is length * breadth. So, 10 m * 6 m = 60 m².
MCQ 20. If the perimeter of a square garden is 36 meters, what is the length of one side of the garden?
- A. 6 m
- B. 9 m
- C. 12 m
- D. 18 m
Answer: B. 9 m — The perimeter of a square is 4 * side. If the perimeter is 36 m, then side = 36 m / 4 = 9 m.
How to Use These Solutions
Attempt each question yourself first and only then compare with the worked answer. Marks in the CBSE board exam are awarded for the METHOD as much as the final result, so reproduce the steps rather than memorising the last line. Where a solution states a law, a formula or a definition, learn that wording — examiners look for it.
Related practice for this chapter: chapter MCQs, previous-year questions, revision notes and sample papers.