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CBSE Class 6 Mathematics Chapter 6 Perimeter and Area Worksheet with Answers

Perimeter and Area form the foundation of mensuration in CBSE Class 6 Mathematics. This printable worksheet offers grade-appropriate practice across multiple question formats—MCQs, fill-in-the-blanks, matching, short and long answers, plus a case study—all aligned with NCERT textbook terminology. Print it, set a timer for 60 minutes, and attempt all sections to build confidence and accuracy for your school exams.

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Key takeaways

  • ✓Worksheet covers all NCERT Class 6 Mathematics Chapter 6 topics: perimeter, area of rectangles and squares, irregular shapes, and unit conversions
  • ✓Difficulty level is foundational to intermediate, matching CBSE Class 6 board expectations and internal exams
  • ✓Suggested completion time is 60 minutes under exam conditions for full benefit
  • ✓Six-section structure progresses from MCQs and objective questions to HOTS and case-study problems
  • ✓Complete answer key with step-by-step explanations helps students self-assess and learn from mistakes
  • ✓Practice questions emphasise real-world applications like fencing gardens, tiling floors, and measuring land
  • ✓Ideal revision tool before unit tests, term exams, or as daily homework for Chapter 6 mastery

Chapter Recap: Perimeter and Area (Class 6 Mathematics)

Chapter 6 in the NCERT Class 6 Mathematics textbook introduces two fundamental measurements of plane figures. Perimeter is the total distance around the boundary of a closed figure, measured in linear units like centimetres or metres. For a rectangle, perimeter equals 2×(length + breadth); for a square, it is 4×side. Area measures the surface enclosed within a boundary, expressed in square units such as cm² or m². The area of a rectangle is length × breadth, while a square's area is side × side. The chapter also teaches how to estimate the area of irregular shapes by counting unit squares on a grid, where each full square counts as 1 unit² and partial squares are approximated. Understanding unit conversions—for instance, 1 m² equals 10,000 cm²—is critical for solving real-world problems involving land, floors, and gardens. Mastery of these concepts prepares students for more advanced mensuration in later classes.
  • Perimeter: total boundary length of a polygon, measured in cm, m, or km
  • Rectangle perimeter = 2(l + b); square perimeter = 4s
  • Area: space inside a shape, measured in cm², m², or hectares
  • Rectangle area = l × b; square area = s²
  • Irregular shapes: count full and approximate half squares on a grid
  • Unit conversions: 1 m = 100 cm, so 1 m² = 10,000 cm²

Worksheet Instructions and Difficulty Level

This worksheet is designed for CBSE Class 6 students who have completed NCERT Chapter 6 Perimeter and Area. The difficulty level is foundational to intermediate, mirroring the style and scope of CBSE internal assessments and term exams. Section A contains six multiple-choice questions testing conceptual understanding and quick calculation. Section B has five fill-in-the-blank items focusing on definitions, formulas, and unit conversions. Section C offers a true/false set to check common misconceptions. Section D presents five short-answer questions (2–3 marks each) requiring formula application and brief reasoning. Section E includes three long-answer or Higher Order Thinking Skills questions (4–5 marks) that blend multiple concepts or real-world scenarios. Finally, one case-study question integrates data interpretation with perimeter and area calculations. The entire worksheet should be completed in 60 minutes under exam-like conditions. Use a pencil, ruler, and eraser; show all working clearly. After finishing, check your answers against the detailed answer key provided at the end to identify gaps and reinforce learning.
  • Suggested time: 60 minutes (strict exam timing for best practice)
  • Difficulty: foundational to intermediate, aligned with CBSE Class 6 standards
  • Materials needed: pencil, eraser, ruler, and notebook for rough work
  • Attempt all sections in order; do not skip questions
  • Show complete working for every numerical problem
  • Review the answer key immediately after completion to maximise learning

Section A: Multiple Choice Questions (1 mark each)

Choose the correct option for each of the following six questions. Each MCQ carries 1 mark. Circle or tick your chosen answer clearly. These questions test your recall of formulas, ability to compute perimeter and area quickly, and understanding of unit conversions. Pay attention to the units given in each question and convert if necessary before calculating. Remember that perimeter is always in linear units (cm, m) while area is in square units (cm², m²). Read every option carefully—some distractors differ by a small calculation error. Attempt all six even if you are unsure; educated guesses can help you learn. After completing Section A, move immediately to Section B without reviewing answers until the full worksheet is done. This simulates real exam pressure and builds time-management skills. Do not use a calculator unless explicitly allowed by your teacher. Show rough work in the margin or on a separate sheet so you can trace mistakes when checking the answer key later. These MCQs are designed to cover perimeter of squares and rectangles, area calculations, and simple unit conversions.
  • Q1. The perimeter of a square with side 9 cm is: (a) 18 cm (b) 27 cm (c) 36 cm (d) 81 cm
  • Q2. Area of a rectangle 15 m long and 8 m wide is: (a) 46 m² (b) 120 m² (c) 23 m² (d) 92 m²
  • Q3. If perimeter of a rectangle is 50 cm and length is 15 cm, breadth is: (a) 10 cm (b) 20 cm (c) 5 cm (d) 35 cm
  • Q4. 1 m² equals: (a) 100 cm² (b) 1,000 cm² (c) 10,000 cm² (d) 1,00,000 cm²
  • Q5. A square garden has area 64 m². Its perimeter is: (a) 16 m (b) 32 m (c) 8 m (d) 64 m
  • Q6. Which has greater perimeter: a rectangle 10 cm × 5 cm or a square of side 7 cm? (a) Rectangle (b) Square (c) Both equal (d) Cannot determine

Section B: Fill in the Blanks (1 mark each)

Complete each sentence by writing the correct word, number, formula, or unit in the blank space provided. This section tests your understanding of key terminology, formulas, and unit conversions introduced in NCERT Class 6 Mathematics Chapter 6. Pay close attention to units—write 'cm' for linear measures and 'cm²' for area. Spelling and notation matter: write formulas clearly using standard mathematical symbols. For instance, perimeter of a rectangle should be written as 2(l + b) or 2 × (length + breadth), not in words. Each blank carries 1 mark, so even a small error costs a point. If you are unsure, skip and return after finishing other sections; sometimes later questions trigger memory. Do not leave blanks empty—attempt every item. These five items cover perimeter formulas, area definitions, unit conversions, and properties of squares and rectangles. Use a sharp pencil so corrections are easy. Avoid over-thinking; most blanks require direct recall from the chapter. Review your NCERT Class 6 Mathematics notes before attempting this section if you are practising at home. After completing all five, double-check units and formula notation before moving to Section C.
  • Q7. Perimeter of a rectangle = 2 × (________ + breadth).
  • Q8. The area of a square with side 's' is equal to ________.
  • Q9. 1 square metre = ________ square centimetres.
  • Q10. A figure that has all four sides equal and all angles 90° is called a ________.
  • Q11. The boundary length of any closed figure is known as its ________.

Section C: True or False (1 mark each)

Read each statement carefully and write 'True' or 'False' in the space provided. If a statement is false, you may be asked to correct it in your answer sheet—check your teacher's instructions. This section targets common misconceptions about perimeter and area that many Class 6 students hold. For instance, confusing perimeter (linear measure) with area (square measure), or assuming that doubling the side of a square doubles its area (it actually quadruples it). Each item carries 1 mark. There is no negative marking, so answer every question even if uncertain. Use logical reasoning: if the units do not match, the statement is likely false. Read numbers and units precisely—'50 cm' is not the same as '50 cm²'. These five true/false items also reinforce unit conversions and formula recall. After writing your answers, revisit any statement that felt confusing and verify against NCERT definitions. This section typically takes 3–5 minutes; do not spend more than 1 minute per item. Move confidently to Section D once done. True/false questions are an excellent quick revision tool before exams because they expose hidden gaps in understanding.
  • Q12. Perimeter and area of a rectangle are always measured in the same units. (True / False)
  • Q13. The area of a square with side 10 cm is 40 cm². (True / False)
  • Q14. If the length of a rectangle is doubled, its perimeter also doubles. (True / False)
  • Q15. 5 m² is greater than 50,000 cm². (True / False)
  • Q16. A rectangle and a square can have the same perimeter but different areas. (True / False)

Section D: Short Answer Questions (2 marks each)

Answer the following five questions in 2–3 sentences or show clear numerical working. Each question carries 2 marks: typically 1 mark for method and 1 mark for the correct final answer. Write units at every step and box or underline your final answer. These short-answer questions require you to apply perimeter and area formulas to straightforward problems, perform unit conversions, or solve for an unknown dimension when perimeter or area is given. Use the formulas you revised in the chapter recap: for rectangles, P = 2(l + b) and A = l × b; for squares, P = 4s and A = s². Show all working even if the calculation seems simple—partial marks are awarded for correct method even if the final answer has a small arithmetic slip. If a question asks for both perimeter and area, compute them separately and label clearly. Pay attention to whether the question specifies 'find the perimeter' or 'find the area'—answering the wrong one earns zero marks. Budget roughly 2 minutes per question in this section. If stuck, move to the next question and return later. These problems mirror the exercise questions in your NCERT Class 6 Mathematics textbook and are common in CBSE internal exams.
  • Q17. A rectangular park is 25 m long and 18 m wide. Find its perimeter.
  • Q18. The side of a square tile is 12 cm. What is its area in cm²?
  • Q19. A rectangle has perimeter 60 cm and breadth 10 cm. Find its length.
  • Q20. Convert 3 m² into square centimetres.
  • Q21. A square lawn has perimeter 48 m. Find the length of one side and then calculate its area.

Section E: Long Answer and HOTS Questions (4 marks each)

Attempt the following three questions with detailed step-by-step solutions. Each question carries 4 marks and tests Higher Order Thinking Skills, multi-step reasoning, or real-world application of perimeter and area. You may need to combine two or more formulas, convert units mid-solution, or interpret a word problem carefully to identify what is given and what is asked. Marks are distributed as follows: 1 mark for correct identification of formula or method, 2 marks for accurate calculation steps, and 1 mark for the final answer with correct unit. Write neatly and organise your solution into clear steps—use headings like 'Given', 'To Find', 'Formula', 'Solution', and 'Answer'. Draw diagrams if they help you visualise the problem; a labelled rectangle or square can clarify dimensions. These questions often involve comparing two shapes, finding cost based on area (for example, cost of fencing or tiling), or working backwards from area to find a dimension. Show all conversions explicitly—if the problem gives dimensions in metres but asks for area in cm², convert at the appropriate step. Spend about 5–6 minutes per question. If a question has two parts, answer both to earn full marks. These HOTS items prepare you for the trickier problems in CBSE term exams and Olympiads.
  • Q22. A rectangular garden is 30 m long and 20 m wide. It is surrounded by a path 2 m wide on all sides. Find the area of the path.
  • Q23. The cost of fencing a square field at ₹15 per metre is ₹1,200. Find the side of the field and then calculate its area.
  • Q24. Two rectangles have the same perimeter of 40 cm. One is 12 cm long; the other is a square. Find the area of each and state which has the greater area.

Section F: Case Study Question (4 marks)

Read the case study below carefully and answer the sub-questions that follow. This integrated question simulates real-life scenarios where perimeter and area concepts are applied together. Case studies have become a regular feature in CBSE exam papers from 2021 onwards, so practising them is essential. You will be given a short paragraph describing a situation—such as designing a garden, planning a floor layout, or comparing plots of land—followed by three or four sub-questions worth 1 mark each. The total for this case study is 4 marks. Read the passage twice to ensure you understand all given data. Underline or highlight key numbers and units. Each sub-question typically asks you to calculate perimeter, area, cost, or a comparative measure. Show working for every sub-question even if it is short. Units must be consistent—convert where necessary. Answer in the order given and label your answers Q25(i), Q25(ii), and so on. Budget 8–10 minutes for the entire case study. These questions test your ability to extract relevant information, choose the correct formula, and apply it accurately under a real-world context.

Complete Answer Key with Explanations

Below are the correct answers for every question in this worksheet, along with brief explanations or working. Use this key only after you have attempted the entire worksheet under timed conditions. Self-assessment is a powerful learning tool—mark your own paper honestly, note the mistakes, and revisit the relevant NCERT sections for concepts you got wrong. For MCQs and objective questions, the correct option or word is given. For numerical questions, step-by-step working is provided so you can identify exactly where a mistake occurred. If you scored below 60 per cent, revise Chapter 6 thoroughly and re-attempt the worksheet after two days. If you scored above 80 per cent, you are well-prepared for school exams; consider challenging yourself with additional HOTS problems or previous years' CBSE question papers. Keep this answer key handy during revision—it doubles as a quick reference guide for formulas and common problem types. Parents can use this key to support home practice without needing a separate teacher guide. For any question where the explanation is unclear, refer back to the NCERT Class 6 Mathematics textbook pages on perimeter and area, or consult your class notes.
  • A1. (c) 36 cm — Perimeter of square = 4 × side = 4 × 9 = 36 cm.
  • A2. (b) 120 m² — Area = length × breadth = 15 × 8 = 120 m².
  • A3. (a) 10 cm — Perimeter = 2(l + b) ⇒ 50 = 2(15 + b) ⇒ 25 = 15 + b ⇒ b = 10 cm.
  • A4. (c) 10,000 cm² — 1 m = 100 cm, so 1 m² = 100 × 100 = 10,000 cm².
  • A5. (b) 32 m — Area = s² ⇒ 64 = s² ⇒ s = 8 m; Perimeter = 4 × 8 = 32 m.
  • A6. (a) Rectangle — Rectangle perimeter = 2(10+5) = 30 cm; square perimeter = 4×7 = 28 cm. Rectangle is greater.
  • A7. length
  • A8. s² or side × side
  • A9. 10,000
  • A10. square
  • A11. perimeter
  • A12. False — Perimeter is in cm or m; area is in cm² or m².
  • A13. False — Area = 10 × 10 = 100 cm², not 40 cm².
  • A14. False — If length doubles, perimeter increases but does not exactly double unless breadth is zero (impossible).
  • A15. False — 5 m² = 5 × 10,000 = 50,000 cm², so both are equal.
  • A16. True — Example: rectangle 10×5 has P=30, A=50; square side 7.5 has P=30, A=56.25.
  • A17. Perimeter = 2(25 + 18) = 2 × 43 = 86 m.
  • A18. Area = 12 × 12 = 144 cm².
  • A19. 60 = 2(l + 10) ⇒ 30 = l + 10 ⇒ l = 20 cm.
  • A20. 3 m² = 3 × 10,000 = 30,000 cm².
  • A21. Perimeter = 48 ⇒ 4s = 48 ⇒ s = 12 m; Area = 12² = 144 m².
  • A22. Outer dimensions = (30+4) × (20+4) = 34 × 24 = 816 m²; Garden area = 30×20 = 600 m²; Path area = 816−600 = 216 m².
  • A23. Perimeter = 1,200 ÷ 15 = 80 m; 4s = 80 ⇒ s = 20 m; Area = 20² = 400 m².
  • A24. First rectangle: 2(12+b)=40 ⇒ 12+b=20 ⇒ b=8; A=12×8=96 cm². Square: 4s=40 ⇒ s=10; A=10²=100 cm². Square has greater area.
  • A25(i). Perimeter = 2(50+30) = 160 m.
  • A25(ii). Area = 50×30 = 1,500 m².
  • A25(iii). Fencing cost = 160 × 25 = ₹4,000.
  • A25(iv). Grass cost = 1,500 × 10 = ₹15,000.

How CBSETUTOR.ai Supports Chapter 6 Mastery

While worksheets like this one provide excellent structured practice, many Class 6 students benefit from on-demand doubt-clearing and step-by-step guidance—especially when parents are busy or local tuition is expensive. CBSETUTOR.ai offers every CBSE student in Classes 6 to 12 a personal AI tutor available 24×7 at a flat ₹999 per month, covering all subjects. Simply snap a photo of any perimeter or area problem from your textbook, worksheet, or exam paper, upload it to the platform, and receive an instant worked solution with explanations in simple language. The AI identifies exactly which formula to use, shows every calculation step, highlights common mistakes, and suggests similar practice questions to reinforce the concept. Parents appreciate the transparent pricing—one subscription works across all classes and subjects, no hidden charges or per-question fees. Students love the freedom to learn at their own pace, replay solutions, and ask follow-up questions without fear of judgement. A 3-day free trial lets your child explore the platform risk-free. Whether your child is stuck on Section E HOTS questions or needs a quick formula refresher before the term exam, CBSETUTOR.ai delivers instant, high-quality academic support that complements school teaching and home practice perfectly.
  • 24×7 AI tutor for CBSE Classes 6–12, all subjects under one subscription
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Frequently asked questions

What topics from NCERT Class 6 Mathematics Chapter 6 does this worksheet cover?+
This worksheet covers all key topics: perimeter of rectangles and squares, area of rectangles and squares, estimating area of irregular shapes using grids, and unit conversions between cm² and m².
How much time should my child take to complete this worksheet?+
Ideally 60 minutes under exam-like conditions. Encourage your child to attempt all sections without breaks, then review answers using the detailed key provided at the end.
Is this worksheet aligned with the latest CBSE Class 6 Mathematics syllabus?+
Yes. It follows NCERT terminology and question patterns, mirrors the style of CBSE internal assessments, and includes the case-study format introduced in recent board guidelines.
Can I print this worksheet for offline practice?+
Absolutely. This page is designed to be printer-friendly. Copy the questions into a Word document or print directly, leaving space for answers. The answer key can be printed separately.
What is the difficulty level of Section E HOTS questions?+
Section E is intermediate to challenging for Class 6. Questions require multi-step reasoning, real-world application, or working backwards from perimeter or area to find unknown dimensions.
How should my child use the answer key effectively?+
Attempt the entire worksheet first without peeking. Then check answers one section at a time, noting mistakes and reviewing the NCERT chapter for any concept that was unclear or incorrect.
Does the worksheet include the case-study question format?+
Yes. Section F contains a 4-mark case study with sub-questions, mirroring the competency-based format now common in CBSE exams from Classes 6 onwards.
Are unit conversions between cm² and m² tested in this worksheet?+
Yes. Multiple questions in Sections A, B, D, and E require converting square metres to square centimetres and vice versa, reinforcing the key conversion: 1 m² = 10,000 cm².
What if my child struggles with perimeter and area word problems?+
Encourage reading each problem twice, underlining given data, and sketching a labelled diagram. Platforms like CBSETUTOR.ai offer instant photo-upload doubt solving to guide students step-by-step through tricky word problems.
Can this worksheet be used for revision before the Class 6 term exam?+
Definitely. It is an ideal revision tool. Completing it under timed conditions simulates exam pressure, and the detailed answer key helps identify weak areas for targeted last-minute revision.

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