Class 6 Maths · Chapter 6
Short answer:
NCERT Class 6 Maths Ganita Prakash Chapter 6 — Perimeter and Area ka ye solution guide poore chapter ko cover karta hai — perimeter of rectangle, square, triangle aur closed shapes; area by counting squares (grid method); area of rectangle aur square with formula; aur real-life applications jaise fencing, boundary aur floor tiling ke sawaal. Har concept step-by-step CBSE marking-scheme style solve kiya gaya hai.
Chapter 6 — Perimeter and Area — Class 6 Ganita Prakash ka wo chapter hai jahan geometry pehli baar measurement se milti hai. Ye chapter poore Class 6 aur aage Class 7-8 Mensuration ki neev hai — jo formula yahan seedhe (rectangle, square) sikhaya jaata hai, wahi aage triangle, parallelogram, circle tak extend hota hai.
Is chapter me do alag-alag ideas hain jo students often confuse kar dete hain: perimeter (boundary ki total length, ek 1-dimensional measurement, unit cm/m me) aur area (surface ka size, ek 2-dimensional measurement, unit cm²/m² me). NCERT is chapter me pehle grid paper pe squares gin kar area samjhaata hai, phir formula introduce karta hai — taaki students formula ko ratt-ke na, samajh kar yaad rakhein.
Ye guide NCERT Ganita Prakash ke har exercise ka step-by-step solution deta hai, common mistakes highlight karta hai, aur exam-relevant important questions bhi cover karta hai.
Chapter 6 Summary — 5 Minute Revision
Chapter 6 ke teen core ideas: (1) Perimeter = boundary ke sabhi sides ka sum — rectangle ke liye 2 × (length + breadth), square ke liye 4 × side. (2) Area = surface cover karne wali space ki quantity — grid pe counting se shuru hoke rectangle formula (length × breadth) aur square formula (side × side) tak. (3) Real-life application — fencing (perimeter) vs flooring/painting (area) me farak samajhna, aur composite/irregular shapes ka perimeter-area estimate karna.
Jo student is chapter me consistently galti karta hai wo aksar unit confuse karta hai (cm vs cm²) ya perimeter-area formula swap kar deta hai. In-text, exercise aur mistakes section me ye sab specifically cover kiya gaya hai.
In-Text Questions — Solutions
Figure it out (Page-based): Ek rectangle ki length 8 cm aur breadth 5 cm hai. Iska perimeter nikalo.
Hal:
Perimeter of rectangle = 2 × (length + breadth)
= 2 × (8 + 5) cm
= 2 × 13 cm
= 26 cm
Answer: Perimeter = 26 cm
Grid paper pe di gayi ek irregular figure me 12 pure squares aur 6 half-se-zyada squares hain (baaki chhoti squares ignore karte hain). Area ka estimate batao.
Hal: Grid method me hum ye rule follow karte hain — jo square half se zyada bhara hai use 1 poora count karo, half se kam ko ignore karo, exactly half ko 1/2 count karo.
Estimated area = Pure squares + (half-se-zyada squares × 1)
= 12 + 6 = 18 square units
Answer: Approximate area ≈ 18 square units
Ek square field ki side 15 m hai. Uske around fencing lagani hai. Total fencing wire kitni chahiye?
Hal: Fencing hamesha perimeter se related hota hai, area se nahi — kyunki wire boundary ke around jaata hai.
Perimeter of square = 4 × side
= 4 × 15 m = 60 m
Answer: 60 m fencing wire chahiye
Ek rectangle jiska perimeter 40 cm hai aur length 12 cm hai, uski breadth nikalo.
Hal:
Perimeter = 2 × (length + breadth)
40 = 2 × (12 + breadth)
20 = 12 + breadth
breadth = 20 − 12 = 8 cm
Answer: Breadth = 8 cm
Exercise Questions — Solutions (Q1–Q6)
1. Ek rectangular park ki length 25 m aur breadth 18 m hai. Uska perimeter aur area dono nikalo.
Hal:
Perimeter:
Perimeter = 2 × (length + breadth) = 2 × (25 + 18) = 2 × 43 = 86 m
Area:
Area = length × breadth = 25 × 18 = 450 m²
Answer: Perimeter = 86 m, Area = 450 m²
2. Ek square room ki area 144 m² hai. Uski side aur perimeter nikalo.
Hal:
Area = side × side, isliye side = √Area
side = √144 = 12 m
Perimeter = 4 × side = 4 × 12 = 48 m
Answer: Side = 12 m, Perimeter = 48 m
3. Ek rectangular sheet ki length breadth se 6 cm zyada hai. Agar breadth 9 cm ho, to sheet ka perimeter aur area nikalo.
Hal:
Length = breadth + 6 = 9 + 6 = 15 cm
Perimeter = 2 × (15 + 9) = 2 × 24 = 48 cm
Area = 15 × 9 = 135 cm²
Answer: Perimeter = 48 cm, Area = 135 cm²
4. Ek square aur ek rectangle ka perimeter same (32 cm) hai. Rectangle ki length 10 cm hai. Batao dono me se kiska area zyada hoga.
Hal:
Square: side = perimeter ÷ 4 = 32 ÷ 4 = 8 cm
Area of square = 8 × 8 = 64 cm²
Rectangle: Perimeter = 2 × (length + breadth)
32 = 2 × (10 + breadth) ⇒ breadth = 6 cm
Area of rectangle = 10 × 6 = 60 cm²
Answer: Square ka area (64 cm²) rectangle ke area (60 cm²) se zyada hai — same perimeter pe square hamesha max area deta hai.
5. Ek L-shape (composite figure) ko do rectangles me todo: Rectangle A (6 cm × 4 cm) aur Rectangle B (3 cm × 2 cm). Total area nikalo.
Hal:
Composite figures ka area unke chhote-chhote regular parts ka area jodkar milta hai.
Area of A = 6 × 4 = 24 cm²
Area of B = 3 × 2 = 6 cm²
Total area = 24 + 6 = 30 cm²
Answer: Total area = 30 cm²
6. Ek square garden ki side 20 m hai. Beech me 4 m chaudi ek seedhi rasta (path) poore garden ko cross karti hai (edge to edge). Path ka area nikalo.
Hal: Path ki length garden ki side ke barabar hogi kyunki wo edge se edge tak jaati hai.
Area of path = length × width = 20 × 4 = 80 m²
Answer: Path ka area = 80 m²
Important Equations — Ek Nazar Me
| Shape | Perimeter | Area |
|---|---|---|
| Rectangle | 2 × (length + breadth) | length × breadth |
| Square | 4 × side | side × side (side²) |
| Triangle | Sum of all three sides | ½ × base × height (Class 7+ me detail) |
| Irregular closed figure | Sum of all boundary sides | Grid counting method (pure squares + half-se-zyada squares) |
| Regular polygon | Number of sides × length of one side | — (varies by shape) |
↔ Table ko side me swipe karein
Common Mistakes — Yahan Marks Kat te Hain
- Perimeter aur area ke units confuse karna — perimeter cm/m me hota hai (1-dimensional), area cm²/m² me (2-dimensional). 'cm²' likhna bhool jaana ya perimeter me square unit likh dena common galti hai.
- Rectangle ka formula galat yaad rakhna — area ko '2 × (l+b)' aur perimeter ko 'l × b' samajh lena, jabki ye ulta hai.
- Grid method me half-se-kam squares ko bhi count kar lena, jabki NCERT rule hai: half se zyada ko 1 gino, half se kam ko ignore karo, exact half ko ½ gino.
- Composite/irregular figures me kisi ek part ka area bhool jaana ya same region ko do baar count kar lena.
- Real-life problems me fencing (perimeter) aur flooring/carpet/paint (area) ko swap kar dena — jaise fencing ke sawaal me area formula laga dena.
- Square ka side nikalte waqt area se square root lena bhool jaana — 'Area = 144 hai to side = 144' likh dena, jabki side = √144 = 12 hona chahiye.
Board-Style Important Questions
- Ek rectangular field ki fencing ka total cost nikalne wala word problem (perimeter-based application) school tests me frequently aata hai.
- Same perimeter ke square aur rectangle ka area compare karne wala conceptual question kai baar pucha jaata hai.
- Grid paper pe di gayi irregular figure ka area estimate karna (counting squares method) ek standard practical-skill question hai.
- Composite figures (L-shape, plus-shape) ka total perimeter ya area nikalna multi-step problem ke roop me common hai.
- Missing side/breadth find-out karna jab perimeter aur ek dimension diya ho — reverse-application type question.
Aksar Poochhe Jaane Wale Sawaal
Perimeter aur area me kya farak hai?
Perimeter kisi bhi closed shape ki boundary ki total length hoti hai (1-dimensional, unit cm/m). Area us shape ke andar ki poori surface ki quantity hoti hai (2-dimensional, unit cm²/m²). Simple yaad rakhne ka tareeka: fencing = perimeter, flooring/painting = area.
Rectangle ka perimeter aur area ka formula kya hai?
Perimeter of rectangle = 2 × (length + breadth)
Area of rectangle = length × breadth
Irregular shape ka area kaise nikalte hain?
Grid paper pe shape ko draw karke squares count karte hain — jo square half se zyada bhara ho use 1 poora gino, half se kam ko ignore karo, aur exactly half ko ½ count karo. Ye estimation method NCERT Chapter 6 me sikhaaya jaata hai.
NCERT Class 6 Maths Ganita Prakash PDF kahan se download karein?
NCERT Class 6 Maths Ganita Prakash ki official PDF ncert.nic.in ki website se download ki ja sakti hai — ye current rationalised syllabus wali textbook hai.
Same perimeter waale do shapes ka area same hota hai kya?
Nahi. Same perimeter ke saath alag-alag shapes ka area alag ho sakta hai. Jaise 32 cm perimeter wale square (side 8 cm) ka area 64 cm² hoga, lekin usi perimeter wale rectangle (10 cm × 6 cm) ka area sirf 60 cm² hoga. Isliye same perimeter pe square hamesha maximum area deta hai.
Class 6 Maths me kaunse chapters is chapter se related hain?
Chapter 6 (Perimeter and Area) Chapter 8 (Playing with Constructions — jahan compass-ruler se shapes banti hain) aur Chapter 9 (Symmetry) se conceptually judta hai, kyunki teeno chapters shapes aur unki properties par based hain. Ye foundation Class 7-8 ke Mensuration chapters (circle, parallelogram, trapezium ka area) ke liye zaroori hai.
Class 6 Maths — Saare Chapters
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