Perimeter is the total distance around a closed figure. Area is the measure of the region enclosed by that figure. Both are measured using standard units: cm, m, sq cm, sq m. Class 6 Maths Chapter 6 Perimeter and Area is from the Ganita Prakash textbook, CBSE 2026 edition.
Important questions class 6 maths chapter 6 on this page cover every question type students face in school exams: missing-side problems, fencing and tiling costs, wire-to-shape conversions, area of triangles, grid estimation, tangram comparisons, and house-plan puzzles.
A student who knows the three perimeter formulas cold and understands that the same area can produce different perimeters will handle every question pattern in this chapter. Most marks are lost on cost problems and composite area questions. All questions and answers are available section by section below.
Key Takeaways
| Topic |
Formula / Key Fact |
| Perimeter of Rectangle |
2 x (length + breadth) |
| Perimeter of Square |
4 x side |
| Perimeter of Triangle |
Sum of all three sides |
| Perimeter of Regular Polygon |
Number of sides x length of one side |
| Area of Rectangle |
length x breadth |
| Area of Square |
side x side |
| Area of Triangle |
Half the area of the enclosing rectangle |
| Same area, different perimeter |
Possible — shape arrangement changes perimeter |
| Grid area estimation |
Count full squares; ignore less than half; count more than half as 1 |
Introduction to Perimeter and Area: Class 6 Chapter 6
Before this chapter, students measured length and counted shapes. Chapter 6 asks a different question: how much space does a boundary take, and how much region does a shape cover?
Perimeter and area look similar but measure completely different things. A thin rectangle and a compact square can have the same area but very different perimeters. The chapter builds this distinction through real-life examples: fencing fields, laying carpets, tiling floors, and planning house layouts.
For every question in this chapter, identify first whether it asks for perimeter (boundary) or area (region). That single step prevents the most common exam mistake.
Important Questions on Perimeter: Class 6 Maths Chapter 6
Perimeter questions in this chapter come in three forms: find the missing side, find the total fencing cost, or find how many rounds cover a distance. These perimeter and area class 6 important questions cover all three types with full solutions.
Perimeter of Rectangle Class 6 Questions
Perimeter of rectangle class 6 questions appear in every school test. The formula is 2 x (length + breadth). Use it to find perimeter, or rearrange it to find a missing side.
Q1. Find the missing terms.
- Perimeter of a rectangle = 14 cm; breadth = 2 cm; length = ? b. Perimeter of a rectangle = 12 m; length = 3 m; breadth = ?
- 2 x (length + 2) = 14 → length + 2 = 7 → length = 5 cm. b. 2 x (3 + breadth) = 12 → 3 + breadth = 6 → breadth = 3 m.
Q2. Akshi wants to put lace all around a rectangular tablecloth 3 m long and 2 m wide. Find the length of lace required. Perimeter = 2 x (3 + 2) = 2 x 5 = 10 m.
Q3. What would be the cost of fencing a rectangular park 150 m long and 120 m wide at Rs 40 per metre? Perimeter = 2 x (150 + 120) = 540 m. Cost = 540 x 40 = Rs 21,600.
Q4. A farmer has a rectangular field 230 m long and 160 m wide. He wants to fence it with 3 rounds of rope. What is the total length of rope needed? Perimeter = 2 x (230 + 160) = 780 m. Total rope = 3 x 780 = 2,340 m.
Perimeter of a Square Questions
Q5. Perimeter of a square = 20 cm. Find the side length. Side = 20 / 4 = 5 cm.
Q6. A piece of string is 36 cm long. What is the length of each side if it forms:
- A square. b. An equilateral triangle. c. A regular hexagon.
- 36 / 4 = 9 cm. b. 36 / 3 = 12 cm. c. 36 / 6 = 6 cm.
Perimeter of a Triangle Questions
Q7. Find the length of the third side of a triangle with perimeter 55 cm and two sides of 20 cm and 14 cm. Third side = 55 - 20 - 14 = 21 cm.
Q8. A triangle has sides 4 cm, 5 cm and 7 cm. Find its perimeter. Perimeter = 4 + 5 + 7 = 16 cm.
Perimeter of a Regular Polygon Questions
Q9. Write the general formula for the perimeter of a regular polygon. Perimeter = Number of sides x Length of one side.
Q10. Write the perimeters of figures on a dot grid in terms of straight (s) and diagonal (d) units. From the textbook figures: 8s + 2d, 4s + 6d, 12s + 6d, 18s + 6d. A diagonal unit is always longer than a straight unit. A figure with diagonal sides has a larger perimeter than it appears when counting only grid squares.
Fencing and Tiling Questions Class 6: Tracks and Rounds
These are the most exam-relevant applied perimeter questions in the chapter. Fencing and tiling questions class 6 students encounter most often use the Akshi and Toshi rectangular tracks as the main model.
Q11. Akshi runs 5 rounds on an outer rectangular track 70 m long and 40 m wide. How far does she run? Perimeter = 2 x (70 + 40) = 220 m. Total = 5 x 220 = 1,100 m.
Q12. Toshi runs 7 rounds on an inner track 60 m long and 30 m wide. Who ran more? Perimeter = 2 x (60 + 30) = 180 m. Total = 7 x 180 = 1,260 m. Toshi ran more.
Q13. Usha takes three rounds of a square park of side 75 m. Find the total distance. Perimeter = 4 x 75 = 300 m. Total = 3 x 300 = 900 m.
Q14. A rectangle with sides 5 cm and 3 cm is made from wire. The wire is straightened and bent into a square. What is the side of the square? Perimeter of rectangle = 2 x (5 + 3) = 16 cm. Side of square = 16 / 4 = 4 cm.
Important Questions on Area: Class 6 Maths Chapter 6
Area questions in this chapter go beyond direct formula use. These class 6 perimeter and area question answers include subtraction problems (carpet, flower beds), cost of tiling, finding width from area, and composite figure splitting.
Area of Rectangle Class 6 Questions
Area of rectangle class 6 questions test both direct calculation and working backwards from a given area to find a missing dimension.
Q15. The area of a rectangular garden 25 m long is 300 sq m. What is the width? Width = 300 / 25 = 12 m.
Q16. The area of a rectangular garden 50 m long is 1,000 sq m. Find the width. Width = 1000 / 50 = 20 m.
Q17. What is the cost of tiling a rectangular plot 500 m long and 200 m wide at Rs 8 per 100 sq m? Area = 500 x 200 = 1,00,000 sq m. Cost = (1,00,000 / 100) x 8 = Rs 8,000.
Q18. A rectangular coconut grove is 100 m long and 50 m wide. Each coconut tree needs 25 sq m. What is the maximum number of trees? Area = 100 x 50 = 5,000 sq m. Number of trees = 5000 / 25 = 200.
Area of a Square Questions
Q19. A floor is 5 m long and 4 m wide. A square carpet of side 3 m is laid on the floor. Find the uncarpeted area. Area of floor = 5 x 4 = 20 sq m. Area of carpet = 3 x 3 = 9 sq m. Uncarpeted = 20 - 9 = 11 sq m.
Questions on Floor, Carpet and Flower Beds
Q20. Four square flower beds of side 4 m each are placed at the four corners of a plot 12 m long and 10 m wide. Find the remaining area. Area of land = 12 x 10 = 120 sq m. Area of 4 flower beds = 4 x (4 x 4) = 64 sq m. Remaining = 120 - 64 = 56 sq m.
Q21. Four flower beds 2 m long and 1 m wide are dug at the four corners of a garden 15 m long and 12 m wide. How much area is available for a lawn? Area of garden = 15 x 12 = 180 sq m. Area of 4 flower beds = 4 x (2 x 1) = 8 sq m. Available = 180 - 8 = 172 sq m.
Q22. By splitting figures into rectangles, find the areas (textbook page 138 figures). Figure a: 28 sq m. Figure b: 9 sq m.
Area of Triangle Class 6 Questions
Area of triangle class 6 questions are based on one key relationship from the Ganita Prakash textbook: a triangle is always half the area of its enclosing rectangle.
Q23. What is the relationship between the area of a triangle and its enclosing rectangle? A triangle drawn on one diagonal of a rectangle has exactly half the area of that rectangle. Area of triangle = 1/2 x base x height.
Q24. Find the areas of the figures on the grid (textbook page 144). a: 24 sq units. b: 30 sq units. c: 48 sq units. d: 16 sq units. e: 12 sq units.
Grid-Based Area Questions: Class 6 Perimeter and Area
Grid questions appear in the Ganita Prakash textbook as estimation exercises. These perimeter and area class 6 extra questions follow four counting rules: one full square = 1 sq unit; less than half = ignore; more than half = count as 1; exactly half = count as 1/2.
Q25. Find the area of the four figures on the dot-grid (textbook page 140). 4 sq units, 9 sq units, 10 sq units, 11 sq units.
Q26. On a squared grid (1 sq = 1 sq unit), make rectangles with area 24 sq units.
- Which rectangle has the greatest perimeter? b. Which rectangle has the least perimeter?
- A 1 x 24 rectangle has the greatest perimeter: 2 x (1 + 24) = 50 units. b. A 4 x 6 rectangle has the least perimeter: 2 x (4 + 6) = 20 units. The closer a rectangle is to a square shape, the smaller its perimeter for the same area.
Tangram and Shape Comparison Questions: Perimeter and Area Class 6
The tangram section teaches area comparison without formulas, by placing shapes over each other. These questions test reasoning.
Q27. In the Class 6 tangram, Shapes A and B have the same area. Shapes C and E have the same area. Shape D can be exactly covered by Shapes C and E together. What does that tell you? Shape D has twice the area of Shape C. Shape D has twice the area of Shape E.
Q28. What is the area of the big square formed with all 7 tangram pieces, in terms of Shape C? The full square has area = 16 times the area of Shape C.
Q29. Shape A has area 18 sq units and Shape B has area 20 sq units. Shape A has a longer perimeter than Shape B. Draw two such shapes. Shape A: 2 m x 9 m. Perimeter = 22 m. Area = 18 sq m. Shape B: 4 m x 5 m. Perimeter = 18 m. Area = 20 sq m. Shape A has smaller area but larger perimeter. This confirms the chapter's key lesson: same area does not mean same perimeter.
Same Area, Different Perimeter Questions
This is one of the most important conceptual sections in the chapter. A compact square-like shape has a smaller perimeter for the same area. A stretched thin rectangle has a larger perimeter.
Q30. Using 9 unit squares, find:
- The smallest possible perimeter. b. The largest possible perimeter. c. Make a figure with a perimeter of 18 units.
- Arrange as a 3 x 3 square. Perimeter = 12 units. b. Arrange as a 1 x 9 rectangle. Perimeter = 20 units. c. Multiple L-shaped or step arrangements give 18 units.
Q31. A square piece of paper is folded in half and cut into two rectangles. Which statement is always true?
- Area of each rectangle is larger than the area of the square. b. Perimeter of the square is greater than both rectangles added. c. Perimeters of both rectangles added is always 1.5 times the perimeter of the square. d. Area of the square is always three times the area of both rectangles added.
Option c is correct. If square has side s: perimeter of square = 4s. Each rectangle is s x s/2, with perimeter = 3s. Two rectangles combined = 6s = 1.5 x 4s.
House Plan and Area Puzzle Questions
These questions test whether students can work backwards from given areas to find missing dimensions inside composite floor plans. They are among the highest-order questions in the class 6 maths chapter 6 important questions with answers set.
Q32. Charan's house plan (textbook page 146). Given: Master bedroom 15 ft x 15 ft, kitchen 15 ft x 12 ft, toilet 5 ft x 10 ft. Total plot width = 30 ft.
Small bedroom: 15 ft x 12 ft = 180 sq ft. Utility: 15 ft x 3 ft = 45 sq ft. Hall: 20 ft x 12 ft = 240 sq ft. Parking: 15 ft x 3 ft = 45 sq ft. Garden: 20 ft x 3 ft = 60 sq ft. Total area = 35 ft x 30 ft = 1,050 sq ft.
Q33. Sharan's house plan (textbook page 147). Given: Master bedroom 12 ft x 15 ft, kitchen 18 ft x 10 ft, small bedroom 12 ft x 10 ft, utility area = 70 sq ft. Total plot width = 42 ft.
Utility: 7 ft x 10 ft = 70 sq ft. Toilet: 5 ft x 10 ft = 50 sq ft. Hall: 23 ft x 15 ft = 345 sq ft. Entrance: 7 ft x 15 ft = 105 sq ft. Total area = 42 ft x 25 ft = 1,050 sq ft.
Both houses have the same area (1,050 sq ft) but different perimeters. Charan's house: 130 ft. Sharan's house: 134 ft. Same area, different perimeter — the chapter's central idea applied to real floor plans.
Area Maze Puzzle Questions: Class 6 Maths Chapter 6
Area maze puzzles ask students to find a missing area or side length from a composite figure where other regions are already labelled. These are HOTS-level questions that appear in CBSE 2026 school assessments.
Q34. Solve the four area maze puzzles (textbook page 148). a. Missing area = 30 sq cm. b. Missing area = 9 sq cm. c. Missing area = 16 sq cm. d. Missing side = 5 cm.
Class 6 Perimeter and Area Worksheet Questions: Extra Practice
These class 6 perimeter and area worksheet questions are additional items based on textbook patterns. Use them to test preparation before CBSE 2026 school exams.
Q35. Give the dimensions of a rectangle whose area equals the sum of areas of two rectangles measuring 5 m x 10 m and 2 m x 7 m. Sum of areas = 50 + 14 = 64 sq m. Possible dimensions: 8 m x 8 m, or 16 m x 4 m, or 32 m x 2 m.
Q36. A square sheet of metal is cut into four equal smaller squares. Which is always true?
- Area of each smaller square is four times the original. b. Perimeter of each smaller square equals the original. c. Total perimeter of all four smaller squares is twice the original perimeter. d. Area of original is smaller than the sum of the four.
Option c is correct. If original side = s, each smaller square has side s/2. Perimeter of each = 4 x (s/2) = 2s. Four squares: 4 x 2s = 8s. Original perimeter = 4s. So 8s = 2 x 4s.
Q37. A wire of length 24 cm is bent into a rectangle with one side measuring 8 cm. What is the other side? 2 x (8 + w) = 24 → 8 + w = 12 → w = 4 cm.
Q38. A rectangular field has perimeter 64 m and length 20 m. What is the width? 2 x (20 + w) = 64 → 20 + w = 32 → w = 12 m.
Class 6 Maths Chapter 6 Short Questions with Answers
These class 6 maths chapter 6 short questions are direct one-step items suited for 1-mark exam practice.
Q39. Area of a square with side 7 cm? 7 x 7 = 49 sq cm.
Q40. Perimeter of a rectangle with length 9 m and breadth 4 m? 2 x (9 + 4) = 26 m.
Q41. Area of a rectangle with length 6 m and breadth 5 m? 6 x 5 = 30 sq m.
Q42. Side of a square with perimeter 36 cm? 36 / 4 = 9 cm.
Q43. Perimeter of an equilateral triangle with side 8 cm? 3 x 8 = 24 cm.
Q44. Perimeter of a regular pentagon with side 5 cm? 5 x 5 = 25 cm.
Important Questions Class 6 Maths