Class 6 Chapter 6 Perimeter and Area Worksheet for NCERT Book

Another chapter and again a set of challenging 20 questions from the NCERT Perimeter and Area chapter. Only attempt this worksheet after you have thoroughly completed the entire chapter. We have provided answer keys with hints for each question.

Class 6 Mathematics – Perimeter and Area (NCERT) | Practice Set: Challenging

A. Perimeter

1. A rectangle has length 18 cm and breadth 11 cm. Find its perimeter.
2. The perimeter of a rectangle is 54 cm. Its length is 16 cm.
   Find the breadth.
3. A rectangle of sides 5 cm and 3 cm is made using a wire. The wire is straightened and then bent to form a square.
   Find the side of the square.
4. A triangle has perimeter 55 cm. Two of its sides are 20 cm and 14 cm.
   Find the third side.
5. A string is 36 cm long. Find the length of each side if it forms:
   • (a) a square
   • (b) an equilateral triangle
   • (c) a regular hexagon
6. A rectangular park is 150 m long and 120 m wide. Fencing costs ₹40 per metre.
   Find the total cost of fencing the park once.
7. A farmer has a rectangular field of length 230 m and breadth 160 m.
   He fences it with 3 rounds of rope. Find the total rope length needed.
8. Two rectangular running tracks:
   • Outer track: 70 m by 40 m, runner completes 5 rounds
   • Inner track: 60 m by 30 m, runner completes 7 rounds

   Find:

   • (a) total distance on outer track
   • (b) total distance on inner track
   • (c) who ran more and by how much
9. A regular polygon has 8 sides, each side is 5 cm. Find its perimeter.
   Also write the general formula for the perimeter of a regular polygon.
10. On a dot grid, a triangle’s boundary has 6 straight-unit segments and 3 diagonal-unit segments.
    Its perimeter is written as 6s + 3d.
    If one straight unit is 1 unit and a diagonal unit is greater than 1 unit, decide which is true:
    • (a) Perimeter can be exactly 9 units
    • (b) Perimeter must be more than 9 units

    Give a reason in one or two lines.

B. Perimeter Changes (Joining / Attaching Shapes)

11. Two identical rectangles each of size 6 cm × 2 cm are joined along a common edge of length 2 cm
    to form one combined figure (no overlap).
    Find the perimeter of the new figure.

    Hint: When two shapes share an edge, that shared edge is not part of the outside boundary.

C. Area

12. Fill in the formulas:
    • (a) Area of a rectangle = __________________
    • (b) Area of a square = __________________
13. A floor is 5 m long and 4 m wide. A square carpet of side 3 m is laid on it.
    Find the area of the floor not carpeted.
14. Four square flower beds each of side 4 m are at the four corners of a land that is 12 m × 10 m.
    Find the area of the remaining part of the land.
15. The area of a rectangular garden is 300 m² and its length is 25 m.
    Find its width.
16. Find the cost of tiling a rectangular plot of land 500 m × 200 m
    at the rate of ₹8 per hundred m².
17. A coconut grove is 100 m × 50 m. Each coconut tree needs 25 m².
    Find the maximum number of trees that can be planted.
18. Estimating area on squared paper:
    A closed shape covers:
    • 18 full squares
    • 7 squares with more than half covered
    • 6 squares with less than half covered
    • 4 squares with exactly half covered

    Using the chapter’s rule (count full as 1, more-than-half as 1, less-than-half as 0, exactly-half as 1/2),
    estimate the area in square units.

19. A rectangle is 12 cm × 8 cm. A diagonal divides it into two triangles.
    Find the area of one triangle.

D. Same Area, Different Perimeter (and vice versa)

20. Using exactly 9 unit squares (connected, no holes):
    • (a) What is the smallest perimeter possible?
    • (b) What is the largest perimeter possible?
    • (c) A square paper is folded in half and cut along the fold to make two rectangles. Which statement is always true?
      • (i) Each rectangle has bigger area than the square
      • (ii) Perimeter of square is greater than sum of perimeters of both rectangles
      • (iii) Sum of perimeters of both rectangles is always 1.5 times perimeter of the square
      • (iv) Area of square is three times area of both rectangles together

Class 6 Mathematics – Answer Key

Chapter 6: Perimeter and Area (NCERT) | Answers with brief reasoning

A. Perimeter

1. Perimeter = 2 × (l + b) = 2 × (18 + 11) = 2 × 29 = 58 cm.
2. P = 2(l + b) ⇒ 54 = 2(16 + b) ⇒ 27 = 16 + b ⇒ b = 11 cm.
3. Wire length = perimeter of rectangle = 2(5 + 3) = 16 cm.
   Square perimeter = 16 cm ⇒ side = 16 ÷ 4 = 4 cm.
4. Third side = 55 − (20 + 14) = 55 − 34 = 21 cm.
5. Total string = 36 cm:
   • (a) Square side = 36 ÷ 4 = 9 cm
   • (b) Equilateral triangle side = 36 ÷ 3 = 12 cm
   • (c) Regular hexagon side = 36 ÷ 6 = 6 cm
6. Perimeter = 2(150 + 120) = 2 × 270 = 540 m.
   Cost = 540 × 40 = ₹21,600.
7. Perimeter = 2(230 + 160) = 2 × 390 = 780 m.
   For 3 rounds: 3 × 780 = 2340 m.
8. Outer track perimeter = 2(70 + 40) = 220 m.
   Total in 5 rounds = 5 × 220 = 1100 m.
   
   Inner track perimeter = 2(60 + 30) = 180 m.
   Total in 7 rounds = 7 × 180 = 1260 m.
   
   Inner track runner ran more by 1260 − 1100 = 160 m.
9. Regular polygon perimeter = (number of sides) × (side length).
   Here: 8 × 5 = 40 cm.
   
   General formula: P = n × s.
10. Correct: (b) Perimeter must be more than 9 units.
    
    Reason: 6s + 3d is more than 6(1) + 3(1) because d > 1, so it exceeds 9.

B. Perimeter Changes (Joining / Attaching Shapes)

11. Each rectangle perimeter = 2(6 + 2) = 16 cm.
    Two separate perimeters total = 16 + 16 = 32 cm.
    
    When joined along a common edge of length 2 cm, that edge is counted twice inside, so subtract 2 × 2 = 4 cm.
    
    New perimeter = 32 − 4 = 28 cm.

C. Area

12. • (a) Area of rectangle = length × width
    • (b) Area of square = side × side
13. Area of floor = 5 × 4 = 20 m².
    Area of carpet = 3 × 3 = 9 m².
    Not carpeted = 20 − 9 = 11 m².
14. Area of land = 12 × 10 = 120 m².
    One flower bed = 4 × 4 = 16 m².
    Four beds = 4 × 16 = 64 m².
    Remaining = 120 − 64 = 56 m².
15. Width = Area ÷ Length = 300 ÷ 25 = 12 m.
16. Area = 500 × 200 = 100,000 m².
    Rate = ₹8 per 100 m².
    Number of hundreds = 100,000 ÷ 100 = 1000.
    Cost = 1000 × 8 = ₹8,000.
17. Grove area = 100 × 50 = 5000 m².
    Each tree needs 25 m².
    Max trees = 5000 ÷ 25 = 200.
18. Estimated area = (full) 18 × 1 + (more than half) 7 × 1 + (less than half) 6 × 0 + (exactly half) 4 × (1/2)
    
    = 18 + 7 + 0 + 2 = 27 square units.
19. Rectangle area = 12 × 8 = 96 cm².
    Diagonal makes two equal-area triangles.
    Area of one triangle = 96 ÷ 2 = 48 cm².

D. Same Area, Different Perimeter

20. • (a) Smallest perimeter: Arrange as a 3×3 square.
      Perimeter = 2(3 + 3) = 12 units.
    • (b) Largest perimeter: Arrange as a 9×1 rectangle.
      Perimeter = 2(9 + 1) = 20 units.
    • (c) Correct option: (iii)
      
      If square side = s, square perimeter = 4s.
      After folding, each rectangle is s × (s/2).
      Each rectangle perimeter = 2(s + s/2) = 3s.
      Sum of both rectangles’ perimeters = 3s + 3s = 6s = 1.5 × 4s.

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