Class 6 Maths Chapter 6 Perimeter and Area Practice Paper 2

Class: VI Subject: Mathematics Session: 2025-26 Chapter: 06 - Perimeter and Area Time: 1½ Hours Max. Marks: 40

General Instructions:

1. All questions are compulsory.

2. This question paper contains 20 questions divided into five sections A, B, C, D and E.

3. Section A contains 10 MCQs of 1 mark each.

4. Section B contains 4 questions of 2 marks each.

5. Section C contains 3 questions of 3 marks each.

6. Section D contains 1 question of 5 marks.

7. Section E contains 2 Case Study Based questions of 4 marks each.

SECTION A - Multiple Choice Questions (1 mark each)

1. If a square has perimeter 48 cm, its side is:
(a) 24 cm
(b) 12 cm
(c) 8 cm
(d) 6 cm

2. The area of a rectangle with length 15 m and breadth 10 m is:
(a) 50 sq m
(b) 150 sq m
(c) 25 sq m
(d) 75 sq m

3. A regular hexagon has a perimeter of 48 cm. The length of each side is:
(a) 6 cm
(b) 8 cm
(c) 12 cm
(d) 16 cm

4. The perimeter of a rectangle is 60 m and its length is 18 m. Its breadth is:
(a) 12 m
(b) 10 m
(c) 14 m
(d) 15 m

5. A square garden has an area of 144 sq m. Its perimeter is:
(a) 36 m
(b) 48 m
(c) 72 m
(d) 24 m

6. Two rectangles have the same area. Rectangle A is 20 m × 10 m and Rectangle B is 25 m × b m. The value of b is:
(a) 8 m
(b) 6 m
(c) 10 m
(d) 12 m

7. The length and breadth of a rectangle are doubled. Its area becomes:
(a) Double
(b) Triple
(c) Four times
(d) Same

8. A wire of length 36 cm is bent to form a rectangle with length 10 cm. Its breadth is:
(a) 8 cm
(b) 6 cm
(c) 10 cm
(d) 4 cm

9. The cost of fencing a square plot at ₹20 per metre is ₹2400. The side of the square plot is:
(a) 30 m
(b) 60 m
(c) 20 m
(d) 40 m

10. A rectangular field has the same perimeter as a square field of side 50 m. If the rectangle's length is 60 m, its breadth is:
(a) 40 m
(b) 30 m
(c) 50 m
(d) 35 m

SECTION B - Short Answer Questions (2 marks each)

11. The perimeter of a square is 96 cm. Find its side and area.

12. A rectangular room is 8 m long and 6 m wide. Find the cost of carpeting the room with carpet costing ₹150 per sq m.

13. Ravi runs around a square park of side 75 m. Find the total distance he covers if he completes 4 rounds.

14. The area of a rectangular garden is 300 sq m and its breadth is 12 m. Find its length and perimeter.

SECTION C - Short Answer Questions (3 marks each)

15. A square and a rectangle have the same area of 100 sq m. If the rectangle has length 20 m, find the perimeter of both shapes and identify which has the smaller perimeter.

16. A rectangular field is 100 m long and 80 m wide. A path of width 3 m runs all around outside the field. Find the area of the path.

17. A piece of wire is in the shape of a rectangle 18 cm long and 14 cm wide. If the same wire is rebent into a square, find the side of the square. Which shape encloses more area?

SECTION D - Long Answer Question (5 marks)

18. A rectangular playground is 40 m long and 30 m wide. There is a path of width 2 m running all around inside the playground. The rest is covered with grass.
(a) Find the area of the playground.
(b) Find the dimensions of the inner rectangle.
(c) Find the area covered with grass.
(d) Find the area of the path. (e) Find the cost of maintaining grass at ₹30 per sq m.

SECTION E - Case Study Based Questions (4 marks each)

19. Swimming Pool A rectangular swimming pool is 25 m long and 15 m wide. A tile border of width 1.5 m runs all around outside the pool.
(a) Find the perimeter of the swimming pool. (1 mark)
(b) Find the dimensions of the outer rectangle (including border). (1 mark)
(c) Find the area of the tile border. (1 mark)
(d) Find the cost of tiles at ₹500 per sq m. (1 mark)

20. Farm Plot A farmer has two plots. Plot A is a square with side 40 m. Plot B is a rectangle with length 50 m and breadth 30 m.
(a) Which plot has greater perimeter and by how much? (1 mark)
(b) Which plot has greater area and by how much? (1 mark)
(c) If the farmer wants to fence both plots with 3 rounds of wire, what total length of wire is needed? (1 mark)
(d) Find the total cost at ₹25 per metre. (1 mark) DETAILED ANSWER KEY - PAPER 02

SECTION A - Answers to MCQs

1.
(b) 12 cm Side = Perimeter ÷ 4 = 48 ÷ 4 = 12 cm

2.
(b) 150 sq m Area = length × breadth = 15 × 10 = 150 sq m

3.
(b) 8 cm Side = Perimeter ÷ 6 = 48 ÷ 6 = 8 cm

4.
(a) 12 m 2 × (18 + breadth) = 60 18 + breadth = 30 breadth = 30 - 18 = 12 m

5.
(b) 48 m Side = √144 = 12 m Perimeter = 4 × 12 = 48 m

6.
(a) 8 m Area of A = 20 × 10 = 200 sq m Area of B = 25 × b = 200 b = 200 ÷ 25 = 8 m

7.
(c) Four times Original area = l × b New area = 2l × 2b = 4lb = Four times

8.
(a) 8 cm 2 × (10 + breadth) = 36 10 + breadth = 18 breadth = 8 cm

9.
(a) 30 m Perimeter = 2400 ÷ 20 = 120 m Side = 120 ÷ 4 = 30 m

10.
(a) 40 m Perimeter of square = 4 × 50 = 200 m 2 × (60 + breadth) = 200 60 + breadth = 100 breadth = 40 m

SECTION B - Answers to Short Answer Questions

11. Given: Perimeter = 96 cm Step 1: Side = 96 ÷ 4 = 24 cm Step 2: Area = 24 × 24 = 576 sq cm Answer: Side = 24 cm, Area = 576 sq cm 12. Given: Length = 8 m, Breadth = 6 m, Rate = ₹150 per sq m Step 1: Area = 8 × 6 = 48 sq m Step 2: Cost = 48 × 150 = ₹7200 Answer: Cost of carpeting = ₹7200 13. Given: Side = 75 m, Rounds = 4 Step 1: Perimeter = 4 × 75 = 300 m Step 2: Total distance = 300 × 4 = 1200 m Answer: Total distance = 1200 m 14. Given: Area = 300 sq m, Breadth = 12 m Step 1: Length = 300 ÷ 12 = 25 m Step 2: Perimeter = 2 × (25 + 12) = 2 × 37 = 74 m Answer: Length = 25 m, Perimeter = 74 m

SECTION C - Answers to Short Answer Questions

15. Given: Both have area = 100 sq m, Rectangle length = 20 m For Square: Side = √100 = 10 m Perimeter = 4 × 10 = 40 m For Rectangle: Breadth = 100 ÷ 20 = 5 m Perimeter = 2 × (20 + 5) = 2 × 25 = 50 m Answer: Square has smaller perimeter (40 m) 16. Given: Field = 100 m × 80 m, Path width = 3 m (outside) Step 1: Outer dimensions = (100 + 2×3) × (80 + 2×3) = 106 × 86 Step 2: Area of field = 100 × 80 = 8000 sq m Step 3: Total area (with path) = 106 × 86 = 9116 sq m Step 4: Area of path = 9116 - 8000 = 1116 sq m Answer: Area of path = 1116 sq m 17.

Given: Rectangle = 18 cm × 14 cm Step 1: Perimeter = 2 × (18 + 14) = 64 cm Step 2: Side of square = 64 ÷ 4 = 16 cm Step 3: Area of rectangle = 18 × 14 = 252 sq cm Step 4: Area of square = 16 × 16 = 256 sq cm Answer: Side = 16 cm, Square encloses more area (by 4 sq cm)

SECTION D - Answer to Long Answer Question

18. Given: Playground = 40 m × 30 m, Path width = 2 m (inside)
(a) Area of playground: Area = 40 × 30 = 1200 sq m
(b) Dimensions of inner rectangle: Length = 40 - 2 × 2 = 36 m Breadth = 30 - 2 × 2 = 26 m Dimensions: 36 m × 26 m
(c) Area covered with grass: Area = 36 × 26 = 936 sq m
(d) Area of path: Area = 1200 - 936 = 264 sq m (e) Cost of maintaining grass: Cost = 936 × 30 = ₹28,080

Answers: (a) 1200 sq m, (b) 36 m × 26 m, (c) 936 sq m, (d) 264 sq m, (e) ₹28,080

SECTION E - Answers to Case Study Based Questions

19.
(a) Perimeter of swimming pool: Perimeter = 2 × (25 + 15) = 2 × 40 = 80 m
(b) Dimensions of outer rectangle: Length = 25 + 2 × 1.5 = 28 m Breadth = 15 + 2 × 1.5 = 18 m Dimensions: 28 m × 18 m
(c) Area of tile border: Area of pool = 25 × 15 = 375 sq m Total area = 28 × 18 = 504 sq m Border area = 504 - 375 = 129 sq m
(d) Cost of tiles: Cost = 129 × 500 = ₹64,500

Answers: (a) 80 m, (b) 28 m × 18 m, (c) 129 sq m, (d) ₹64,500

20.
(a) Comparing perimeters: Plot A: 4 × 40 = 160 m Plot B: 2 × (50 + 30) = 160 m Both have equal perimeter
(b) Comparing areas: Plot A: 40 × 40 = 1600 sq m Plot B: 50 × 30 = 1500 sq m Plot A is greater by 100 sq m
(c) Total length of wire: Total perimeter = 160 + 160 = 320 m Wire needed = 320 × 3 = 960 m
(d) Total cost: Cost = 960 × 25 = ₹24,000

Answers: (a) Equal, (b) Plot A by 100 sq m, (c) 960 m, (d) ₹24,000