Trapezium Ka Area | Class 8 Maths Book 2 Ch 7

📘 Class 8 · Ganita Prakash Book 2Ch 7 · AreaPost 7 / 8⏱ 25–30 min

Trapezium Ka Area ⏢

IS POST MEIN

Pehle Yeh Aata Hai?Kahani Concept Deep Concept Examples Real Life Galti 10 MCQs FAQs Practice HOTS Olympiad Recap

✅ Pehle Yeh Aata Hai?

Yeh post shuru karne se pehle, in teen sawaalon ko 1 minute mein khud try kijiye:

Trapezium mein kitni jodi parallel sides?
½ × 4 × (6 + 10) = ?
Parallelogram area?

Answers dekho

Ek jodi
32
Base × height

Teeno sahi? Badhiya! Parallelogram: Post 5.

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🎬 Kahani: Khet Ki Medh

Golu ke chacha ka khet ek trapezium tha: sadak wali side 36 m, nadi wali side 24 m (dono parallel), beech ki doori 14 m.

“Isme rectangle bhi nahi, triangle bhi nahi!” Golu pareshan. Priya boli, “Ek ulti copy saath jodo, parallelogram ban jaayega!” ⏢

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📖 Concept: Area = ½ × h × (a + b)

Step 1: Do copies ka jaadu

Trapezium + ulti copy = parallelogram (base a + b, height h).

Trapezium (parallel sides a, b, doori h) ki ulti copy saath jodo: parallelogram, base (a + b), height h. Area h(a + b). Ek trapezium = aadha:

Area = ½ × h × (a + b)

Step 2: Rectangle + triangles se

Upar ki side a ke kono se neeche perpendiculars: beech mein rectangle (a × h), dono taraf triangles (½xh, ½yh) jahan x + y = b − a. Jod: ah + ½(b − a)h = ½h(a + b) ✅

Step 3: Parallelogram + triangle

Ek kone se doosri tirchhi side ke parallel line: parallelogram (a × h) + triangle (½(b − a)h). Wahi jawab.

Step 4: Matlab

½(a + b) = parallel sides ka average. Area = average lambaai × height. Khet: ½ × 14 × (36 + 24) = 420 m².

Step 5: Special cases

a = b → parallelogram (h × a). a = 0 → triangle (½ h b). Ek formula, teen shapes!

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🔐 Deep Concept: Trapezium Ko Rectangle Mein (Śulba-Sūtra)

Isosceles trapezium ko rectangle mein badalna: dono tirchhi sides ke midpoints se seedhi khadi line kheencho, kone ke triangles kaat ke upar ghuma do. Ban gaya rectangle, lambaai = ½(a + b), height h!

Vedi banane wale yahi karte the. Is tarah 144 cm² ka trapezium bhi banaa sakte: jaise h = 12, a + b = 24 (a = 8, b = 16). 🔐

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✏️ Solved Examples

Example 1 (Easy): a = 10, b = 14, h = 6?

½ × 6 × 24 = 72.

WHY sahi hai? Average 12 × 6 ✅

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Example 2 (Medium): Khet 36 m, 24 m, h 14 m?

420 m².

WHY sahi hai? 30 × 14 ✅

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Example 3 (NCERT style): Hexagon ko trapezium, equilateral triangle, rhombus mein: area ka anupaat?

6 chhote equilateral triangles gino: trapezium 3, triangle 1, rhombus 2 → 3 : 1 : 2.

WHY sahi hai? Jod 6 ✅

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Priya ka mantra: “Average lambaai × height!” 🎉

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🏠 Real Life Mein

🌾 Khet ki medh, nahar ka cross-section.
🪣 Balti ka side view.
🏠 Chhat ki dhalaan.
🛤️ Rail track ke neeche mitti ka dher.

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🧭 Kab Use Karein, Kab Nahi

Situation	Kya karein	Kyun
Ek jodi parallel	✅ ½ h (a + b)	Trapezium
a = b	✅ Parallelogram	a × h
a = 0	✅ Triangle	½ b h
Tirchhi sides jodi	❌ Galat	Parallel sides chahiye

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❌→✅ Worked Mistake

Sawaal: Parallel 8, 12; tirchhi 5; h 4. Area?

❌ Galat: “½ × 5 × 20 = 50.”

Galti kya hai? Tirchhi side ko height ❌

✅ Sahi: ½ × 4 × 20 = 40.

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📝 10 MCQs

Q1. Area?

(a) ½ h (a + b)

(b) h (a + b)

(c) ½ ab

(d) a + b + h

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Parallelogram (double).
(c) galat: Nahi.
(d) galat: Nahi.

Q2. 10, 14, h 6?

(a) 72

(b) 144

(c) 36

(d) 30

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

Q3. 36, 24, 14?

(a) 420

(b) 840

(c) 60

(d) 74

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Double.
(c) galat: Nahi.
(d) galat: Nahi.

Q4. Do copies se?

(a) Parallelogram

(b) Triangle

(c) Circle

(d) Square hamesha

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

Q5. a = 0?

(a) Triangle

(b) Rectangle

(c) Square

(d) Kuch nahi

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

Q6. ½(a + b)?

(a) Average lambaai

(b) Height

(c) Perimeter

(d) Diagonal

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

Q7. 8, 12, h 4?

(a) 40

(b) 80

(c) 50

(d) 20

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Nahi.
(c) galat: Tirchhi.
(d) galat: Nahi.

Q8. Hexagon anupaat?

(a) 3 : 1 : 2

(b) 1 : 1 : 1

(c) 2 : 1 : 3

(d) 3 : 2 : 1

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

Q9. Area 144, h 12, a + b?

(a) 24

(b) 12

(c) 144

(d) 6

Solution dekho

Sahi jawab: (a)

(a) sahi: 288 ÷ 12 ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

Q10. a = 10, b = 6, h = 14?

(a) 112

(b) 224

(c) 30

(d) 84

Solution dekho

Sahi jawab: (a)

(a) sahi: ½ × 14 × 16 ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

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❓ FAQs (Bachchon Ke Asli Sawaal)

1. Trapezium ki height?

Parallel sides ke beech 90° doori.

2. Isosceles trapezium?

Tirchhi sides barabar.

3. Teen tareeke same jawab?

Haan, sab ½ h (a + b).

4. Area se height?

2A ÷ (a + b).

5. Rectangle trapezium?

Haan (do jodi parallel), formula chalta.

6. ZYXW wala (A midpoint) sawaal?

Midpoint se triangle banake area same dikhaate; kaat-jod ka idea.

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🏋️ Practice Zone (12 Sawaal)

Q1. Easy 5, 9, h 4?

Solution dekho

28.

Q2. Easy 12, 18, h 10?

Solution dekho

150.

Q3. Easy a = b = 7, h 3?

Solution dekho

21.

Q4. Easy a = 0, b = 10, h 6?

Solution dekho

30.

Q5. Medium Area 60, a 7, b 13. h?

Solution dekho

Q6. Medium Area 90, h 9, a 4. b?

Solution dekho

16.

Q7. Medium 24 m, 36 m, 14 m?

Solution dekho

420 m².

Q8. NCERT style Do copies wala tareeka samjhao.

Solution dekho

Parallelogram (a + b) × h ka aadha.

Q9. NCERT style 144 cm² ka trapezium banao.

Solution dekho

h 12, a 8, b 16 (ek udaharan).

Q10. Medium Isosceles: 10, 22, tirchhi 10. h?

Solution dekho

(22−10)/2 = 6 → √(100 − 36) = 8; area 128.

Q11. Medium Hexagon ratio.

Solution dekho

3 : 1 : 2.

Q12. NCERT style Rectangle → trapezium (same area)?

Solution dekho

Ek kone se triangle kaat ke doosri taraf ulta jodo.

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🧠 HOTS (Sochne Wale Sawaal)

Q1. a aur b dono double, h same?

Solution dekho

Area double.

Q2. h double?

Solution dekho

Area double.

Q3. Trapezium ko ek diagonal se kaatein to do triangles ka area?

Solution dekho

½ h a aur ½ h b: anupaat a : b.

Q4. Triangle formula trapezium se kaise?

Solution dekho

a = 0.

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🏆 Olympiad Corner

Q1. Isosceles 6, 14, tirchhi 5. Area?

Solution dekho

h = 3 → ½ × 3 × 20 = 30.

Q2. Area 100, a : b = 2 : 3, h 8?

Solution dekho

a + b = 25 → 10, 15.

Q3. Right trapezium 4, 10, h 8. Tirchhi side?

Solution dekho

√(36 + 64) = 10.

Q4. Trapezium ke diagonals se bane 4 triangles mein do (tirchhi sides ke paas) ka area?

Solution dekho

Barabar!

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💗 CharuMam Motivation

Golu ko ek ajeeb shape mili, Priya ne usse jaani-pehchaani bana diya. ⏢

Nayi cheez se dar ho to use kisi purani dost (shape) se jodo. Har naya topic purane ka hi bada roop hai! 🌱

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🟢 Master Recap

Trapezium: ek jodi parallel sides a, b; doori h.
Area = ½ × h × (a + b).
Do copies → parallelogram; ya rectangle + triangles.
a = b → parallelogram; a = 0 → triangle.
Śulba: isosceles trapezium → rectangle.

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👉 Aage Kya?

Aakhri post: asli duniya ke units: inch, foot, acre, bigha aur badlaav! 📏

← Pichla: Post 6 — Rhombus Ka Area 📚 Chapter 7 ke saare posts Agla: Post 8 — Area Real Life Mein: Units Aur Badlaav →

Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬

✅ Pehle Yeh Aata Hai?

🎬 Kahani: Khet Ki Medh

📖 Concept: Area = ½ × h × (a + b)

Step 1: Do copies ka jaadu

Step 2: Rectangle + triangles se

Step 3: Parallelogram + triangle

Step 4: Matlab

Step 5: Special cases

🔐 Deep Concept: Trapezium Ko Rectangle Mein (Śulba-Sūtra)

✏️ Solved Examples

🏠 Real Life Mein

🧭 Kab Use Karein, Kab Nahi

❌→✅ Worked Mistake

📝 10 MCQs

❓ FAQs (Bachchon Ke Asli Sawaal)

🏋️ Practice Zone (12 Sawaal)

🧠 HOTS (Sochne Wale Sawaal)

🏆 Olympiad Corner

💗 CharuMam Motivation

🟢 Master Recap

👉 Aage Kya?

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