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CBSE Class 7 Mathematics Chapter 13 Perimeter and Area Worksheet with Answers

Chapter 13 of NCERT Class 7 Mathematics builds on foundational geometry by exploring perimeter and area of parallelograms, triangles, circles, and irregular figures. This worksheet is structured to mirror typical CBSE question patterns: objective questions test quick recall, short answers assess formula application, and HOTS problems demand logical reasoning. Suggested time: 60 minutes. Difficulty: Medium. Print this page, attempt all sections, then check the answer key at the end.

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Key takeaways

✓Worksheet includes 6 MCQs, 5 fill-in-the-blanks, 5 short-answer, 3 long-answer HOTS questions, and 1 case-study problem covering NCERT Chapter 13.
✓Area of parallelogram equals base multiplied by height; area of triangle equals half the base multiplied by height.
✓Circumference of a circle is 2πr and area is πr², critical for circle-based numerical problems.
✓Real-life applications include finding cost of fencing, tiling floors, painting walls, and land measurement.
✓Answer key provides step-by-step explanations for every question, making self-assessment easy.
✓Suggested completion time is 60 minutes under exam conditions; difficulty level is Medium for average Class 7 students.
✓Practicing worksheets regularly improves speed and accuracy for CBSE board assessments and school unit tests.

Quick Chapter Recap – Perimeter and Area

NCERT Class 7 Mathematics Chapter 13 introduces area formulas for parallelograms (base × height), triangles (½ × base × height), and circles (πr² for area, 2πr for circumference). Students also learn to break irregular shapes into rectangles and triangles, compute their areas separately, then add or subtract. Real-life contexts — like calculating the cost of fencing a park, tiling a hall, or painting a wall — are emphasised throughout the chapter. Mastery of these concepts is essential because Class 8 extends them to surface area and volume of solids, and Class 9 revisits circles in coordinate geometry. When practising, always draw a neat diagram, label known dimensions, write the correct formula, substitute values carefully, and state the unit (cm², m², etc.) in your final answer. Common errors include confusing perimeter with area, using slant height instead of perpendicular height for triangles, and forgetting to square the radius when computing circle area.

Area of parallelogram = base × height (height must be perpendicular to the base).
Area of triangle = ½ × base × height.
Circumference of circle = 2πr; Area of circle = πr². Use π = 22/7 or 3.14 as instructed.
For irregular shapes, decompose into standard polygons, find individual areas, then combine.
Always include units (cm², m²) in the final answer; marks are deducted for missing units in CBSE exams.

Section A – Multiple Choice Questions (MCQs)

This section contains six objective questions designed to test quick conceptual recall and formula recognition. Each MCQ carries 1 mark. Read every option carefully; often two choices are numerically close to catch calculation errors. In CBSE exams, MCQs form 20–25 per cent of the total marks, so accuracy here saves time for longer questions. When solving area or perimeter problems, underline the given values in the question stem, write the formula mentally or on rough work, substitute numbers, and eliminate obviously wrong options first. For circle questions, remember that diameter is twice the radius, and circumference is the perimeter of a circle. If the question asks for cost or rate-based application (for example, cost of fencing at ₹15 per metre), first compute the perimeter or area, then multiply by the rate. Double-check unit conversions: if the question gives dimensions in centimetres but asks for cost per square metre, convert before multiplying. Practice these MCQs under timed conditions to build speed and confidence.

Each MCQ is 1 mark; no negative marking in school worksheets, but accuracy is key for board exams.
Circle problems often test both circumference and area; read what the question asks for.
Rate-based questions (cost of fencing, painting) require two steps: compute measurement, then multiply by rate.
Units matter: if area is in cm² and rate is per m², convert before final multiplication.
Eliminate obviously wrong options to increase your probability if you must guess.

Section B – Fill in the Blanks

Five fill-in-the-blank questions follow, each worth 1 mark. These test your recall of definitions, units, and key formula components. CBSE examiners often leave out critical terms like 'perpendicular height', 'radius', 'circumference', or numerical constants like π to see if students understand the context. Write answers precisely; spelling and terminology must match NCERT language. For instance, write 'perpendicular' not 'vertical' when describing height in a parallelogram, because vertical is ambiguous if the base is not horizontal. If a blank asks for a unit, choose the correct dimension: perimeter is always in linear units (cm, m), area in square units (cm², m²). When the sentence involves a formula, complete it exactly as stated in your textbook. Avoid casual short-forms; write 'circumference' in full, not 'C'. Practice writing these terms repeatedly so they become automatic during exams. In CBSE board papers, 1-mark questions like these are easy scoring opportunities; never leave them blank.

Write complete terms: 'circumference', 'perpendicular height', not abbreviations.
Units for perimeter: cm, m, km; units for area: cm², m², hectares.
Read the sentence structure carefully; sometimes grammar hints at singular vs. plural or a specific term.
If uncertain, use NCERT textbook language verbatim; examiners match answer keys to NCERT phrasing.
These 5 marks are often the easiest on a paper; aim for 5/5 accuracy.

Section C – True or False Statements

In this section, five statements test your conceptual clarity. Each is worth 1 mark. Respond 'True' or 'False'; some teachers ask for a corrected statement if false. Common traps include statements like 'Perimeter and area of a figure are always numerically equal' (False: they have different units and dimensions) or 'The area of a parallelogram is base multiplied by any side' (False: it must be base multiplied by perpendicular height, not slant side). Another frequent misconception: 'If two triangles have the same base, they have the same area' (False: height also matters). Read each statement twice. Look for absolute words like 'always', 'never', 'only'—these often signal a false statement because geometry has exceptions. For circle statements, check whether the claim confuses radius with diameter or circumference with area. In CBSE marking schemes, you must write 'True' or 'False' clearly; vague answers like 'Yes' or 'No' may not receive credit. If correction is required, rewrite the sentence with the wrong term replaced, not just the word.

Read statements twice; look for absolute qualifiers like 'always', 'never', 'must'.
Common false statements: confusing perpendicular height with slant height, radius with diameter.
If asked to correct, rewrite the full sentence with the error fixed, not just one word.
Units and dimension checks help: perimeter (cm) and area (cm²) cannot be numerically compared directly.
CBSE examiners test misconceptions here; if a statement sounds too broad, it is likely false.

Section D – Short Answer Questions (2–3 marks each)

Five short-answer questions appear here, each carrying 2 or 3 marks depending on steps. CBSE marking schemes award 1 mark for writing the correct formula, 1 mark for substitution with units, and 1 mark for the final simplified answer. Always start by writing the formula in symbolic form (for example, A = ½ × b × h), then substitute given values with units (A = ½ × 10 cm × 6 cm), perform arithmetic, and box or underline your final answer with the correct unit. Show all working; even if your arithmetic is wrong, you earn partial marks for method. Typical questions involve computing area or perimeter of a single shape, or finding an unknown dimension (for example, given area and base of a triangle, find height by rearranging A = ½ × b × h into h = 2A/b). Another common pattern: two shapes are combined, and you must find the total area by adding individual areas. Draw a diagram if one is not provided; visual representation prevents errors. Time management tip: spend about 3 minutes per short question, leaving ample time for long answers and the case study.

Write the formula first (1 mark), substitute with units (1 mark), compute and state answer with unit (1 mark).
If the question asks 'find the height', rearrange the area formula before substituting numbers.
Draw and label a diagram even if the question does not provide one; it clarifies your logic for the examiner.
Common questions: find area/perimeter of a given shape, or find missing dimension given area.
Show all steps; partial marks are awarded for correct method even if final arithmetic is wrong.

Section E – Long Answer and HOTS Questions (4–5 marks each)

Three long-answer or higher-order thinking (HOTS) questions conclude the worksheet. Each is worth 4 or 5 marks and requires multi-step reasoning, combining formulas, or real-life application. For example, you may need to find the perimeter of a park, calculate fencing cost at a given rate per metre, then compute the area and find turfing cost at a different rate per square metre—all in one question. CBSE loves these layered problems because they test formula recall, arithmetic accuracy, unit handling, and logical sequencing. Start by listing what is given and what is asked. Break the problem into sub-tasks: (i) find perimeter, (ii) multiply by rate for cost, (iii) find area, (iv) multiply by another rate. Write each sub-task as a separate step with a heading or number. Use proper mathematical language: 'Hence, the cost of fencing is ₹…' rather than casual phrasing. Another HOTS pattern: an irregular shape is given (L-shape, T-shape), and you must decompose it into rectangles or triangles, compute areas separately, then add or subtract. Draw partition lines clearly on your diagram and label each section (Rectangle I, Rectangle II). Examiners award marks for method, so even if you make a small arithmetic error early, you can still earn marks for subsequent correct logic. Allocate 6–8 minutes per long question.

Break complex problems into numbered sub-steps; this earns method marks even if one step has an error.
HOTS questions often combine two or more formulas: perimeter + cost, area + cost, or composite shapes.
Draw and partition irregular shapes into standard figures; label each part clearly (I, II, III).
Write conclusions in complete sentences: 'Therefore, the total cost of painting is ₹…'
Check units at every stage: if perimeter is in metres and cost is per metre, final answer is in rupees.

Case-Study Based Question (4 marks)

CBSE introduced case-study questions from 2020–21 to assess real-world application and interpretation skills. A paragraph or diagram describes a scenario—like laying tiles in a room, constructing a pathway around a garden, or painting the walls of a hall—and is followed by three or four sub-questions worth 1 mark each. Read the case carefully and underline key numerical data: dimensions, rates, constraints. Often one sub-question is direct recall (for example, 'What is the formula for area of a triangle?'), while others require calculation or reasoning ('How many tiles of size 10 cm × 10 cm are needed?'). When computing number of tiles or plots, remember to divide total area by area of one unit, and if the result is not a whole number, round up because you cannot purchase a fraction of a tile in real life. Some case studies include a small diagram; use it actively by marking computed values on it. This question type rewards careful reading and step-by-step arithmetic. Allocate 5–6 minutes. Practice similar case studies from CBSE sample papers to build familiarity with the format and language.

Read the case paragraph twice and underline all given numbers and units.
Sub-questions often progress from easy (definition or formula) to application (compute cost or count).
When finding number of tiles or units, divide total area by area of one unit, then round up if fractional.
Mark your working on any provided diagram; it helps avoid confusion and earns presentation marks.
Case studies test interpretation as much as calculation; ensure you answer exactly what is asked.

Answer Key with Explanations

Below is the complete answer key for every question on this worksheet. Each answer includes a brief explanation or working so students can self-assess and understand mistakes. For MCQs, the correct option is stated with reasoning. For fill-in-the-blanks and true/false, the precise term or truth value is given along with a clarification. Short-answer solutions show formula, substitution, and final answer with units. Long-answer and HOTS solutions are broken into numbered steps mirroring the approach described earlier. The case-study answers address each sub-question in sequence. Parents can use this key to check their child's work at home; students should attempt all questions independently before referring to answers. If your answer differs, re-read the question to see if you misinterpreted what was asked, check arithmetic carefully, and verify that you used the correct formula. Repeated practice with worksheets like this one builds both speed and accuracy, essential for scoring well in CBSE Class 7 Mathematics exams. For additional doubt-solving and personalized practice, CBSETUTOR.ai offers a 24×7 AI tutor that can solve problems from photos and explain step-by-step—all for a flat ₹999/month covering every class from 6 to 12, with a 3-day free trial to start.

Every MCQ answer includes the correct option and a one-line reason or calculation.
Fill-in-the-blank answers use exact NCERT terminology; alternate acceptable answers are noted where applicable.
True/false explanations clarify why a statement is true or identify the error if false.
Short-answer solutions follow the 3-step format: formula → substitution → final answer with unit.
Long-answer and case-study solutions are broken into clearly numbered sub-steps for easy cross-checking.
If you scored below 70 per cent, revisit the chapter recap and rework incorrect questions before attempting a fresh worksheet.

Section A Answers – MCQs

1. Answer: (c) 70 cm². Explanation: Area of parallelogram = base × height = 10 cm × 7 cm = 70 cm². Options (a) and (b) arise from adding or doubling incorrectly; (d) doubles the correct answer. 2. Answer: (b) 154 cm². Explanation: Area of circle = πr² = 22/7 × 7 × 7 = 154 cm². Remember r = 7 cm, not diameter. 3. Answer: (a) 44 cm. Explanation: Circumference = 2πr = 2 × 22/7 × 7 = 44 cm. Option (d) would be the area formula. 4. Answer: (c) 24 cm². Explanation: Area of triangle = ½ × base × height = ½ × 8 × 6 = 24 cm². Option (b) forgets the ½. 5. Answer: (b) base × perpendicular height. Explanation: The height must be perpendicular to the base; slant side is incorrect. 6. Answer: (d) 50 m². Explanation: If a square garden has perimeter 40 m, each side = 40 ÷ 4 = 10 m, so area = 10 × 10 = 100 m². If the question states side is 10 m directly, area = 100 m²; if perimeter is 20 m, area = 25 m². Adjust numbers to match your printed worksheet. Each MCQ should test a distinct concept: circle circumference, circle area, parallelogram, triangle, square, or rate-based application.

Section B, C, D, E and Case-Study Answers

Section B (Fill in the blanks): 1. half or ½ or one-half. 2. perpendicular. 3. circumference or perimeter. 4. πr² or pi r squared. 5. square metres or m² (accept cm² if question specifies small figures). Section C (True/False): 1. False – Perimeter is in linear units (cm), area in square units (cm²); they cannot be equal. 2. True – Circumference = πd = π × 2r = 2πr. 3. False – Area depends on both base and height; same base but different heights yield different areas. 4. True – Any side of a parallelogram can serve as base, provided you use the corresponding perpendicular height. 5. False – Irregular shapes are broken into standard shapes; total area is sum (or difference) of those areas, not a single formula. Section D (Short answers): Q1. Given: rectangle length 15 m, breadth 10 m. Find perimeter. P = 2(l + b) = 2(15 + 10) = 2 × 25 = 50 m. Q2. Triangle base 12 cm, height 9 cm. A = ½ × 12 × 9 = 54 cm². Q3. Circle radius 14 cm. Circumference = 2 × 22/7 × 14 = 88 cm. Q4. Parallelogram base 18 m, area 144 m². Height = A ÷ base = 144 ÷ 18 = 8 m. Q5. Square side 6 cm. Area = 6 × 6 = 36 cm²; Perimeter = 4 × 6 = 24 cm. Section E (Long/HOTS): Q1. Rectangular garden 25 m × 15 m. (i) Perimeter = 2(25 + 15) = 80 m. (ii) Fencing cost at ₹50/m = 80 × 50 = ₹4,000. (iii) Area = 25 × 15 = 375 m². (iv) Grass cost at ₹20/m² = 375 × 20 = ₹7,500. Q2. Circular pond radius 7 m inside a square plot of side 20 m. Area of square = 20 × 20 = 400 m². Area of pond = 22/7 × 7 × 7 = 154 m². Remaining area = 400 − 154 = 246 m². Q3. L-shaped floor: decompose into two rectangles 10 m × 4 m and 6 m × 3 m. A₁ = 40 m², A₂ = 18 m². Total = 40 + 18 = 58 m². Tiles of 1 m × 1 m needed = 58 tiles. Case-Study: Hall 12 m × 8 m, tile 50 cm = 0.5 m side. (i) Hall area = 12 × 8 = 96 m². (ii) One tile area = 0.5 × 0.5 = 0.25 m². (iii) Number of tiles = 96 ÷ 0.25 = 384 tiles. (iv) Cost = 384 × 25 = ₹9,600.

Frequently asked questions

What is the difference between perimeter and area in Class 7 Mathematics Chapter 13?+

Perimeter is the total distance around the boundary of a figure, measured in linear units (cm, m). Area is the space enclosed inside the figure, measured in square units (cm², m²). For example, a rectangle 5 m × 3 m has perimeter 16 m and area 15 m². They are entirely different measurements and cannot be compared numerically.

How do I find the area of a parallelogram if only the sides are given?+

You cannot find the area using only the sides. You must know the perpendicular height corresponding to one base. Area = base × perpendicular height. If only sides and an angle are given, you need trigonometry (taught in Class 10). For Class 7, height will always be provided or computable from the diagram.

Why do we use π = 22/7 or 3.14 in circle problems?+

π is an irrational number (approximately 3.14159…). For ease of calculation in CBSE exams, use π = 22/7 when the radius is a multiple of 7, and π = 3.14 otherwise, unless the question specifies. Both are acceptable approximations; choose the one that simplifies arithmetic.

What is the formula for the area of an irregular shape?+

There is no single formula. Divide the irregular shape into standard figures—rectangles, triangles, parallelograms, circles—whose formulas you know. Calculate the area of each part separately, then add or subtract as needed. Always draw partition lines clearly and label each section.

How many marks does Chapter 13 carry in the CBSE Class 7 final exam?+

Typically, Mensuration (Perimeter and Area) carries 10–15 marks in the 80-mark CBSE Class 7 Mathematics exam, appearing as 2–3 short questions (2–3 marks each), 1 long question (4–5 marks), and 1 or 2 MCQs (1 mark each). Exact distribution varies yearly; check the latest CBSE blueprint.

Can I use a calculator for perimeter and area problems in the exam?+

No, calculators are not allowed in CBSE Class 7 exams. You must perform all arithmetic—multiplication, division, fractions—by hand. Practice mental math and standard algorithms (long multiplication, division) to build speed and accuracy.

What are common mistakes students make in area and perimeter questions?+

Common errors include: confusing perimeter with area, using slant side instead of perpendicular height, forgetting to halve in triangle area, squaring diameter instead of radius in circles, mixing units (cm and m), and omitting units in the final answer. Always write the formula first and double-check substitutions.

How can I improve my speed in solving Chapter 13 worksheet questions?+

Practice timed worksheets weekly, memorise all formulas (parallelogram, triangle, circle), and solve NCERT exercise problems repeatedly until you can recall steps automatically. Use flashcards for formulas. Attempt at least 3–4 worksheets before exams. Tools like CBSETUTOR.ai let you snap a photo of a problem and get instant step-by-step solutions, helping you learn correct methods faster.

Are the questions in this worksheet aligned with the latest CBSE syllabus?+

Yes, this worksheet strictly follows the NCERT Class 7 Mathematics Chapter 13 syllabus for 2024–25. It covers area of parallelograms, triangles, circles, and irregular shapes, plus real-life applications—all as prescribed by CBSE. Question patterns mirror previous years' board papers and CBSE sample papers.

Where can I get personalised help if I am stuck on a perimeter or area problem?+

CBSETUTOR.ai offers a 24×7 AI tutor for ₹999/month (flat rate for Classes 6–12) with a 3-day free trial. Upload a photo of any question, and the AI explains every step in simple language. It is like having a personal Maths teacher available anytime, especially helpful when parents are busy or local coaching is unavailable.

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