Class 8 Maths · Chapter 14
Short answer: Chapter 14 'Area' (Ganita Prakash Part 2) trapezium, parallelogram aur rhombus ka area nikalna, kisi bhi quadrilateral ko diagonal se do triangles me todkar area calculate karna, aur grid paper par irregular shapes ka area estimate karna sikhaata hai — sab formulas + step-by-step solved examples yahan hain.
Chapter 14 poore Ganita Prakash Part 2 ki mensuration understanding ka final aur sabse practical adhyay hai — yahan tak jo triangles, quadrilaterals aur unke properties Part 1-2 me padhe hain, wahi ab real area calculation me use hote hain. "Area" chapter Class 8 Maths (Ganita Prakash Part 2, 2026-27 rationalised session, chapters 8-14) ka 14th aur aakhri chapter hai. Is chapter me trapezium, parallelogram, rhombus jaise quadrilaterals ka area nikalna, kisi bhi general (irregular) quadrilateral ko diagonal se do triangles me todkar area calculate karna, aur grid/graph paper par curved shapes ka area estimate karna sikhaya jaata hai. Yeh chapter isliye important hai kyunki iska application seedha real life me dikhta hai — khet ka area, plot ka area, floor tiling — sab yahi concepts use karte hain.
Chapter 14 Summary — 5 Minute Revision
Chapter 14 'Area' Class 8 Maths Ganita Prakash Part 2 ka aakhri chapter hai, jisme quadrilaterals — trapezium, parallelogram, rhombus — ka area nikalna sikhaya jaata hai. Sabse important concept yeh hai ki koi bhi irregular quadrilateral ek diagonal se do triangles me split karke, dono triangles ka area alag-alag nikalkar jod diya jaata hai. Isके saath grid/graph paper par curved ya irregular boundaries ka area 'aadhon ke rule' se estimate karna bhi sikhaya jaata hai, jo real-life fields ya plots ke liye practical hai. Formula-based questions (trapezium, parallelogram, rhombus) aur application-based word problems (khet, plot, floor area) dono exercise me common hain — dono practice karna zaroori hai.In-Text Questions — Solutions
Ek parallelogram-shaped park ka base 40 m aur height 25 m hai. Iska area nikalo.
Area = base × height = 40 × 25 = 1000 m²
Yeh direct formula-application wala question hai — isme unit (m²) likhna kabhi mat bhoolo.
Kisi trapezium ki dono parallel sides equal ho jaayein, toh woh kaunsa shape ban jaata hai aur formula kaise badalta hai?
Agar dono parallel sides equal ho jaayein toh trapezium ek parallelogram ban jaata hai. Formula ½(a+b)h me jab a = b, toh yeh ½(2a)h = a × h ban jaata hai — jo exactly parallelogram ka formula hai. Isse pata chalta hai ki trapezium ka formula general hai aur parallelogram uska ek special case hai.
Exercise Questions — Solutions (Q1–Q6)
Ek trapezium ki parallel sides 12 cm aur 8 cm hain, aur unke beech ki height 6 cm hai. Trapezium ka area nikalo.
Area = ½ × (a + b) × h
Area = ½ × (12 + 8) × 6
Area = ½ × 20 × 6 = 60 cm²
Ek parallelogram ka base 15 cm hai aur height 7 cm hai. Uska area nikalo.
Area = base × height
Area = 15 × 7 = 105 cm²
Yaad rakho — height hamesha base ke perpendicular distance hoti hai, slant side nahi.
Ek rhombus ke diagonals 10 cm aur 16 cm hain. Area nikalo.
Area = ½ × d₁ × d₂
Area = ½ × 10 × 16 = 80 cm²
Rhombus ka area sirf dono diagonals se nikal jaata hai — side length ki zaroorat nahi.
Ek quadrilateral ABCD ko diagonal AC ne do triangles me baant diya hai. Triangle ABC ka area 18 cm² aur triangle ACD ka area 24 cm² hai. Poore quadrilateral ka area kya hoga?
Area of quadrilateral ABCD = Area(ΔABC) + Area(ΔACD)
= 18 + 24 = 42 cm²
Yehi tareeka hum kisi bhi irregular quadrilateral ke liye use karte hain — usse ek diagonal se do triangles me split karo.
Grid paper par ek trapezium 5 poore squares, 4 aadhe se zyada bhare squares, aur 3 aadhe se kam bhare squares me se guzarta hai (aadhon ka rule use karke). Estimated area batao.
Rule: poore squares poora count, aadhe ya usse zyada wale poora count, aadhe se kam wale ignore.
Estimated area = 5 + 4 = 9 square units
Yeh estimation method curved ya irregular boundaries ke liye useful hai jab exact formula na ho.
Ek trapezium-shaped field ki parallel sides 25 m aur 15 m hain, aur area 400 m² hai. Field ki height (dono parallel sides ke beech ki distance) nikalo.
Area = ½ × (a + b) × h
400 = ½ × (25 + 15) × h
400 = ½ × 40 × h = 20h
h = 400 ÷ 20 = 20 m
Important Equations — Ek Nazar Me
| Shape | Formula | Note |
|---|---|---|
| Parallelogram | Area = base × height | Height = perpendicular distance, slant side nahi |
| Trapezium | Area = ½ × (sum of parallel sides) × height | Dono parallel sides ka average × height |
| Rhombus | Area = ½ × d₁ × d₂ | d₁, d₂ = dono diagonals |
| General Quadrilateral | Area = Area(Δ1) + Area(Δ2) | Ek diagonal se do triangles me split karke dono ka area jodo |
| Irregular/Curved Shape (grid method) | Area ≈ (poore squares) + (half-or-more squares) | Half-se-kam squares ignore karo — estimation ke liye use hota hai |
↔ Table ko side me swipe karein
Common Mistakes — Yahan Marks Kat te Hain
- Trapezium ke formula me height ko slant (tirchi) side samajh lena — height hamesha parallel sides ke beech ka perpendicular distance hota hai, slant side nahi.
- Rhombus ka area nikalte waqt side × side kar dena, jabki rhombus ka area diagonals se nikalta hai: ½ × d₁ × d₂.
- General quadrilateral ka area nikalte waqt sirf ek triangle ka area calculate karke chhod dena — dono triangles (diagonal se bane) ka area jodna zaroori hai.
- Grid paper method me half-se-kam bhare squares ko bhi count kar lena — rule yeh hai ki sirf half-or-more wale squares count hote hain, half-se-kam ignore hote hain.
- Answer likhte waqt area ka unit (cm², m²) likhna bhool jaana — mensuration me unit ke bina answer incomplete maana jaata hai.
- Parallelogram aur trapezium ke formula ko confuse kar dena — parallelogram me sirf ek base hota hai (base × height), trapezium me dono parallel sides ka average lena padta hai.
Board-Style Important Questions
- NCERT/CBSE ke practice papers me trapezium-shaped field ka area diya jaakar unki missing parallel side ya height nikalwane wale questions common hain.
- Rhombus ke diagonals diye jaakar area, ya area aur ek diagonal diye jaakar dusra diagonal nikalwane wale questions practice sets me aate hain.
- Kisi irregular quadrilateral plot ka diagram dekar usse do triangles me split karke poora area nikalwane wale application-based questions dekhe gaye hain.
- Grid/graph paper par diya gaya irregular ya curved shape dekar 'aadhon ke rule' se uska estimated area batane wale questions practice worksheets me common hain.
- Real-life context wale word problems (jaise khet, plot, ya floor ka area, cost-per-square-metre ke saath) is chapter ke exercises me dekhe gaye hain.
Aksar Poochhe Jaane Wale Sawaal
Class 8 Maths Chapter 14 'Area' me kya-kya cover hota hai?
Ye chapter Ganita Prakash Part 2 (Class 8, 2026-27 rationalised session) ka hissa hai. Isme trapezium, parallelogram, rhombus jaise quadrilaterals ka area nikalna, kisi bhi irregular quadrilateral ko diagonal se do triangles me todkar area nikalna, aur grid/graph paper par curved ya irregular shapes ka area estimate karna sikhaya jaata hai.
Ganita Prakash class 8 maths chapter 1 solutions kahan milenge — kya yeh Area chapter se related hai?
Nahi, Chapter 1 'A Square and A Cube' Ganita Prakash Part 1 ka pehla chapter hai (squares, cubes, patterns), jabki Area chapter number 14 hai jo Part 2 ke end me aata hai. Dono alag topics hain — Chapter 1 number theory/patterns pe hai, Chapter 14 mensuration pe.
Class 8 maths new book ka naam kya hai 2026-27 session ke liye?
NCERT ne purani single Class 8 Maths textbook ko hata kar do-part 'Ganita Prakash' (Part 1 aur Part 2) launch kiya hai. Part 1 me chapters 1 se 7 aur Part 2 me chapters 8 se 14 hain — total 14 chapters. Area is naye structure ka aakhri (14th) chapter hai.
Area chapter ke formulas yaad karne ka sabse aasan tareeka kya hai?
Sabse pehle basic shapes ke formula (trapezium, parallelogram, rhombus) ek table banake yaad karo — neeche formulas table dekho. Uske baad practice karo ki koi bhi irregular quadrilateral ko diagonal se do triangles me kaise todte hain, kyunki exam me yehi concept-based questions zyada aate hain, sirf formula-plug-in wale kam.
Trapezium aur parallelogram ke area formula me kya farak hai?
Parallelogram ka area sirf base × height hota hai kyunki dono parallel sides equal hoti hain. Trapezium me dono parallel sides alag-alag length ki hoti hain, isliye unka average lena padta hai: Area = ½ × (sum of parallel sides) × height.
Kya is chapter me curved shapes ka area bhi nikalna sikhaya jaata hai?
Haan, exact formula ke bina curved ya irregular boundary wale shapes ke liye grid/graph paper par 'counting squares' aur 'aadhon ka rule' (jahan half-or-more squares poora count hote hain aur half-se-kam ignore hote hain) use karke estimated area nikalna sikhaya jaata hai — yeh real-life fields, ponds jaise irregular shapes ke liye practical approach hai.
Class 8 Maths — Saare Chapters
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