Class 6 Maths Chapter 6 Perimeter and Area Practice Paper 3

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. A rectangular field is 45 m long and 30 m wide. If it is divided into 15 equal square plots, the side of each square plot is:
(a) 6 m
(b) 9 m
(c) 10 m
(d) 15 m

2. The ratio of the perimeter of a square to its side is:
(a) 1:2
(b) 2:1
(c) 4:1
(d) 1:4

3. The perimeter of a rectangle remains unchanged when its length is increased by 5 cm and breadth is decreased by 5 cm. This is possible when:
(a) Original length equals breadth
(b) The rectangle becomes a square
(c) Always true for any rectangle
(d) Never possible

4. If each side of a square is tripled, its area becomes:
(a) 3 times
(b) 6 times
(c) 9 times
(d) 12 times

5. A wire of length 52 cm is first bent to form a rectangle with length 15 cm. Then it is bent to form a square. The difference in their areas is:
(a) 4 sq cm
(b) 8 sq cm
(c) 16 sq cm
(d) 24 sq cm

6. A rectangular plot 80 m × 60 m has two roads each 5 m wide running through its middle, one parallel to length and one parallel to breadth. The area covered by roads is:
(a) 675 sq m
(b) 700 sq m
(c) 725 sq m
(d) 650 sq m

7. The cost of fencing a circular garden is same as fencing a square garden. If the side of square is 44 m and cost is ₹10 per m, the perimeter of circular garden is:
(a) 132 m
(b) 154 m
(c) 176 m
(d) 198 m

8. The length and breadth of a rectangle are in ratio 5:3. If perimeter is 64 cm, its length is:
(a) 15 cm
(b) 20 cm
(c) 25 cm
(d) 30 cm

9. A rectangular carpet has area 120 sq m and perimeter 46 m. Its length is:
(a) 8 m
(b) 12 m
(c) 15 m
(d) 20 m

10. Two squares have sides in ratio 2:3. The ratio of their areas is:
(a) 2:3
(b) 4:9
(c) 9:4
(d) 3:2

SECTION B - Short Answer Questions (2 marks each)

11. The perimeter of a rectangular field is 82 m and its area is 400 sq m. Find the breadth if length is 25 m. Verify your answer.

12. Find the side of a square whose perimeter equals the perimeter of a rectangle with dimensions 35 m by 25 m. Also compare their areas.

13. A wire when bent in the form of an equilateral triangle encloses an area of 121√3 sq cm. If the same wire is bent to form a square, what will be the area enclosed?

14. The length of a rectangle is twice its breadth. If the perimeter is 72 cm, find its dimensions and area.

SECTION C - Short Answer Questions (3 marks each)

15. A rectangular lawn 80 m by 60 m has two roads each 10 m wide running through its middle, one parallel to length and other to breadth. Find the cost of gravelling the roads at ₹50 per sq m.

16. The perimeter of a square and a rectangle are equal. The rectangle measures 26 cm by 18 cm. Calculate how much the area of square exceeds the area of rectangle.

17. A room is 13 m long and 9 m wide. A square carpet of side 8 m is laid on the floor. Find what fraction of the floor is not carpeted.

SECTION D - Long Answer Question (5 marks)

18. A rectangular park 100 m long and 80 m wide has two paths each 5 m wide running through its middle crossing each other at right angles.
(a) Draw a rough sketch showing the paths.
(b) Find the area of the path running parallel to length.
(c) Find the area of the path running parallel to breadth.
(d) Find the total area of both paths. (Be careful not to count the intersection twice!) (e) If the rest of the park is covered with grass at ₹40 per sq m, find the total cost.

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

19. Cricket Stadium A rectangular cricket stadium is 150 m long and 120 m wide. It has a pavilion on one side measuring 30 m × 20 m and a practice pitch area measuring 40 m × 30 m on the opposite side.
(a) Find the total area of the stadium. (1 mark)
(b) Find the combined area of pavilion and practice pitch. (1 mark)
(c) Find the area available for spectators and players (excluding pavilion and practice area). (1 mark)
(d) If a boundary rope is placed all around the stadium, what length of rope is needed? (1 mark)

20. Tile Pattern A rectangular floor 12 m long and 8 m wide is to be covered with square tiles. Each tile has a side of 40 cm.
(a) Convert the floor dimensions to cm and find the floor area in sq cm. (1 mark)
(b) Find the area of one tile. (1 mark)
(c) How many tiles are needed to cover the entire floor? (1 mark)
(d) If each tile costs ₹25, find the total cost of tiles. (1 mark) DETAILED ANSWER KEY - PAPER 03

SECTION A - Answers to MCQs

1.
(b) 9 m Total area = 45 × 30 = 1350 sq m Area of each plot = 1350 ÷ 15 = 90 sq m Side = √90 ≈ 9 m (considering perfect square division)

2.
(c) 4:1 Perimeter = 4 × side Ratio = 4 × side : side = 4:1

3.
(c) Always true for any rectangle Perimeter = 2(l + b) = 2(l+5 + b-5) = 2(l + b) The changes cancel out in perimeter calculation.

4.
(c) 9 times Original area = a² New area = (3a)² = 9a² = 9 times

5.
(c) 16 sq cm Rectangle: breadth = 26 - 15 = 11 cm, Area = 15 × 11 = 165 sq cm Square: side = 52 ÷ 4 = 13 cm, Area = 169 sq cm Difference = 169 - 165 = 4 sq cm

6.
(a) 675 sq m Road parallel to length = 80 × 5 = 400 sq m Road parallel to breadth = 60 × 5 = 300 sq m Intersection (counted twice) = 5 × 5 = 25 sq m Total = 400 + 300 - 25 = 675 sq m

7.
(c) 176 m Perimeter of square = 4 × 44 = 176 m Since costs are same, perimeters are equal = 176 m

8.
(b) 20 cm Let length = 5x, breadth = 3x 2(5x + 3x) = 64 16x = 64, x = 4 Length = 5 × 4 = 20 cm

9.
(c) 15 m 2(l + b) = 46, so l + b = 23 l × b = 120 Solving: l = 15 m, b = 8 m

10.
(b) 4:9 If sides are 2x and 3x Areas are (2x)² : (3x)² = 4x² : 9x² = 4:9

SECTION B - Answers to Short Answer Questions

11. Given: Perimeter = 82 m, Area = 400 sq m, Length = 25 m Step 1: 2(25 + b) = 82 25 + b = 41 b = 16 m Verification: Area = 25 × 16 = 400 sq m ✓ Answer: Breadth = 16 m 12. Given: Rectangle = 35 m × 25 m Step 1: Perimeter = 2 × (35 + 25) = 120 m Step 2: Side of square = 120 ÷ 4 = 30 m Step 3: Area of square = 900 sq m Step 4: Area of rectangle = 875 sq m Answer: Side = 30 m, Square area is greater by 25 sq m 13. Given: Area of equilateral triangle = 121√3 sq cm Step 1: Using formula: (√3/4)a² = 121√3 a² = 484, a = 22 cm Step 2: Perimeter = 3 × 22 = 66 cm Step 3: Side of square = 66 ÷ 4 = 16.5 cm Step 4: Area = 16.5 × 16.5 = 272.25 sq cm Answer: Area of square = 272.25 sq cm 14.

Given: Length = 2 × breadth, Perimeter = 72 cm Step 1: Let breadth = x, then length = 2x Step 2: 2(2x + x) = 72 6x = 72, x = 12 cm Step 3: Breadth = 12 cm, Length = 24 cm Step 4: Area = 24 × 12 = 288 sq cm Answer: 24 cm × 12 cm, Area = 288 sq cm

SECTION C - Answers to Short Answer Questions

15. Given: Lawn = 80 m × 60 m, Road width = 10 m, Rate = ₹50/sq m Step 1: Road parallel to length = 80 × 10 = 800 sq m Step 2: Road parallel to breadth = 60 × 10 = 600 sq m Step 3: Intersection = 10 × 10 = 100 sq m Step 4: Total road area = 800 + 600 - 100 = 1300 sq m Step 5: Cost = 1300 × 50 = ₹65,000 Answer: Cost = ₹65,000 16. Given: Rectangle = 26 cm × 18 cm, Equal perimeters Step 1: Perimeter = 2 × (26 + 18) = 88 cm Step 2: Side of square = 88 ÷ 4 = 22 cm Step 3: Area of square = 22 × 22 = 484 sq cm Step 4: Area of rectangle = 26 × 18 = 468 sq cm Step 5: Difference = 484 - 468 = 16 sq cm Answer: Square exceeds by 16 sq cm 17.

Given: Room = 13 m × 9 m, Carpet = 8 m × 8 m Step 1: Area of room = 13 × 9 = 117 sq m Step 2: Area of carpet = 8 × 8 = 64 sq m Step 3: Uncarpeted area = 117 - 64 = 53 sq m Step 4: Fraction = 53/117 Answer: 53/117 of the floor is not carpeted

SECTION D - Answer to Long Answer Question

18. Given: Park = 100 m × 80 m, Path width = 5 m (crossing)
(a) Sketch: [Two perpendicular paths crossing in the middle]
(b) Path parallel to length: Area = 100 × 5 = 500 sq m
(c) Path parallel to breadth: Area = 80 × 5 = 400 sq m
(d) Total area of both paths: Intersection = 5 × 5 = 25 sq m Total = 500 + 400 - 25 = 875 sq m (e) Cost of grass: Total park area = 100 × 80 = 8000 sq m Grass area = 8000 - 875 = 7125 sq m Cost = 7125 × 40 = ₹2,85,000

Answers: (b) 500 sq m, (c) 400 sq m, (d) 875 sq m, (e) ₹2,85,000

SECTION E - Answers to Case Study Based Questions

19.
(a) Total area of stadium: Area = 150 × 120 = 18,000 sq m
(b) Combined area of pavilion and practice pitch: Pavilion = 30 × 20 = 600 sq m Practice = 40 × 30 = 1200 sq m Combined = 600 + 1200 = 1800 sq m
(c) Area for spectators and players: Available = 18,000 - 1800 = 16,200 sq m
(d) Length of boundary rope: Perimeter = 2 × (150 + 120) = 540 m

Answers: (a) 18,000 sq m, (b) 1800 sq m, (c) 16,200 sq m, (d) 540 m

20.
(a) Floor dimensions in cm and area: Length = 1200 cm, Breadth = 800 cm Area = 1200 × 800 = 9,60,000 sq cm
(b) Area of one tile: Area = 40 × 40 = 1600 sq cm
(c) Number of tiles needed: Tiles = 9,60,000 ÷ 1600 = 600 tiles
(d) Total cost: Cost = 600 × 25 = ₹15,000

Answers: (a) 9,60,000 sq cm, (b) 1600 sq cm, (c) 600 tiles, (d) ₹15,000