Rhombus Ka Area | Class 8 Maths Book 2 Ch 7

📘 Class 8 · Ganita Prakash Book 2Ch 7 · AreaPost 6 / 8⏱ 25–30 min

Rhombus 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:

Rhombus ki sides kaisi?
Rhombus ke diagonals kaise kaatte?
½ × 20 × 15 = ?

Answers dekho

Saari barabar
Aadha-aadha aur 90° pe
150

Teeno sahi? Badhiya! Parallelogram: Post 5.

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🎬 Kahani: Patang Ka Kaagaz

Makar Sankranti pe Rohan diamond (rhombus) patang bana raha tha. Lambi teeli 20 cm, aadi teeli 15 cm, dono 90° pe. Kitna kaagaz lagega?

Priya: “Patang ke charon taraf ek rectangle socho: 20 × 15 = 300. Patang uska bilkul aadha!” 🪁 = 150 cm².

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📖 Concept: Area = ½ × d₁ × d₂

Step 1: Diagonals 90° pe

Rhombus ke diagonals d₁, d₂ ek-doosre ko aadha karte, 90° pe.

Rhombus ke diagonals ek-doosre ko aadha-aadha aur 90° pe kaatte hain. To 4 barabar right triangles bante, har ek ke legs d₁/2 aur d₂/2.

Step 2: Do triangles se

Diagonal BD rhombus ko do triangles ABD, CBD mein: dono ka base d₂, height d₁/2. Area = 2 × ½ × d₂ × d₁/2 = ½ d₁ d₂.

Step 3: Bahar ka rectangle

Rhombus ke charon taraf rectangle (d₁ × d₂): rhombus uska aadha (4 andar ke triangles = 4 bahar ke). NCERT: rhombus ko kaat ke rectangle WXYZ (d₁ × d₂/2) bhi bana sakte.

Area = ½ × d₁ × d₂

Step 4: Base × height bhi chalega

Rhombus ek parallelogram hai: side × height bhi sahi. Dono tareeke ek jawab dete.

Step 5: Side bhi diagonals se

Side = √((d₁/2)² + (d₂/2)²) (Ch 2). 24 aur 70: side = √(144 + 1225) = 37.

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🔐 Deep Concept: Kite Ka Bhi Yahi Formula

Kite (patang aakaar, do-do sides barabar) mein bhi diagonals 90° pe hote. Isliye kite ka area bhi ½ × d₁ × d₂! Square mein d₁ = d₂ = d: area = d²/2 (Ch 2 ka “diagonal pe square = double” yahi kehta!).

Shart: diagonals perpendicular hon. Rectangle mein nahi hote, to wahan yeh formula galat. 🔐

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✏️ Solved Examples

Example 1 (Easy): Diagonals 20, 15?

½ × 20 × 15 = 150 cm².

WHY sahi hai? Rectangle 300 ka aadha ✅

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Example 2 (Medium): Diagonals 24, 70: area aur side?

Area 840, side 37.

WHY sahi hai? ½ × 24 × 70 = 840 ✅

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Example 3 (NCERT style): Square diagonal 10. Area?

½ × 10 × 10 = 50.

WHY sahi hai? Side √50, side² = 50 ✅

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Rohan ka mantra: “Diagonals ka guna, phir aadha!” 🎉

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🏠 Real Life Mein

🪁 Patang ka kaagaz.
💎 Diamond tiles farsh pe.
🧀 Barfi/kaju katli ke tukde (rhombus!).
🛡️ Jaali aur fence ke design.

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🧭 Kab Use Karein, Kab Nahi

Situation	Kya karein	Kyun
Rhombus, kite, square	✅ ½ d₁ d₂	Diagonals 90° pe
Rectangle (square nahi)	❌ ½ d₁ d₂ nahi	Diagonals 90° nahi
Side pata, height pata	✅ Side × height	Parallelogram
Side diagonals se	✅ Pythagoras	Aadhe diagonals legs

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❌→✅ Worked Mistake

Sawaal: Diagonals 16, 12. Area?

❌ Galat: “16 × 12 = 192.”

Galti kya hai? Aadha karna bhool gaye ❌

✅ Sahi: 96.

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📝 10 MCQs

Q1. Rhombus area?

(a) ½ d₁ d₂

(b) d₁ d₂

(c) d₁ + d₂

(d) 2 d₁ d₂

Solution dekho

Sahi jawab: (a)

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

Q2. 20, 15?

(a) 150

(b) 300

(c) 35

(d) 75

Solution dekho

Sahi jawab: (a)

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

Q3. Diagonals kaise kaatte?

(a) Aadha + 90°

(b) Sirf aadha

(c) Kabhi nahi

(d) 45°

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: 90° bhi.
(c) galat: Nahi.
(d) galat: Nahi.

Q4. 16, 12?

(a) 96

(b) 192

(c) 28

(d) 48

Solution dekho

Sahi jawab: (a)

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

Q5. 24, 70 side?

(a) 37

(b) 47

(c) 94

(d) 74

Solution dekho

Sahi jawab: (a)

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

Q6. Square diag 10?

(a) 50

(b) 100

(c) 25

(d) 20

Solution dekho

Sahi jawab: (a)

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

Q7. Kite area?

(a) ½ d₁ d₂

(b) d₁ d₂

(c) Nahi nikalta

(d) b × h

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Nahi.
(c) galat: Nikalta.
(d) galat: Kite parallelogram nahi.

Q8. Rectangle (6 × 8, diag 10) ka ½ d₁ d₂ = 50 sahi?

(a) Nahi, area 48

(b) Haan

(c) Kabhi

(d) Pata nahi

Solution dekho

Sahi jawab: (a)

(a) sahi: Diagonals 90° nahi ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

Q9. Rhombus side 5, diag 6. Doosra?

(a) 8

(b) 4

(c) 10

(d) 12

Solution dekho

Sahi jawab: (a)

(a) sahi: √(25 − 9) = 4 → 8 ✅
(b) galat: Aadha.
(c) galat: Nahi.
(d) galat: Nahi.

Q10. Uska area?

(a) 24

(b) 48

(c) 30

(d) 12

Solution dekho

Sahi jawab: (a)

(a) sahi: ½ × 6 × 8 ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

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❓ FAQs (Bachchon Ke Asli Sawaal)

1. Rhombus aur square?

Square ek rhombus hai (90° wala).

2. Diagonals barabar?

Sirf square mein.

3. Area 2 tareeke?

½ d₁ d₂ aur side × height.

4. Kite kya?

Do jodi padosi sides barabar.

5. Rectangle ko rhombus mein (dissection)?

Rectangle ke kone ke triangles kaat-ke jodo; khud socho!

6. Units?

cm², m².

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🏋️ Practice Zone (12 Sawaal)

Q1. Easy Diag 10, 8?

Solution dekho

40.

Q2. Easy Diag 30, 16?

Solution dekho

240.

Q3. Easy Square diag 8?

Solution dekho

32.

Q4. Easy Area 60, ek diag 12. Doosra?

Solution dekho

10.

Q5. Medium Diag 16, 30: side?

Solution dekho

√(64 + 225) = 17.

Q6. Medium Side 13, diag 10. Doosra aur area?

Solution dekho

24, 120.

Q7. Medium Kite diag 9, 14?

Solution dekho

63.

Q8. NCERT style Rhombus diag 20, 15.

Solution dekho

150 cm².

Q9. NCERT style ½ d₁ d₂ kyun?

Solution dekho

Bahar ke rectangle ka aadha.

Q10. Medium Side 10, height 8 (rhombus)?

Solution dekho

80.

Q11. Medium Area 96, side 10 (rhombus). Height?

Solution dekho

9.6.

Q12. NCERT style Rectangle ke barabar area ka rhombus kaise?

Solution dekho

Rectangle ki lambaai double karke usi mein midpoints wala rhombus, ya kone ke triangles kaat ke jodo.

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🧠 HOTS (Sochne Wale Sawaal)

Q1. Rhombus ke diagonals double: area?

Solution dekho

4 guna.

Q2. Side same, area sabse zyada kab?

Solution dekho

Square.

Q3. ½ d₁ d₂ = side × height se height?

Solution dekho

h = d₁ d₂ ÷ (2 × side).

Q4. Kya rhombus ke 4 triangles congruent?

Solution dekho

Haan, sab.

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🏆 Olympiad Corner

Q1. Rhombus perimeter 52, diag 10. Area?

Solution dekho

Side 13 → doosra 24 → 120.

Q2. Area 120, diag ka anupaat 5 : 12. Diagonals?

Solution dekho

½ × 5k × 12k = 120 → k = 2 → 10, 24.

Q3. Diagonals ka jod 14, side 5. Area?

Solution dekho

(d₁/2)² + (d₂/2)² = 25, d₁ + d₂ = 14 → 6, 8 → 24.

Q4. Square ka area 50, diag?

Solution dekho

10.

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💗 CharuMam Motivation

Rohan ki patang aasmaan mein, aur uska hisaab zameen pe pakka! 🪁

Masti aur ganit saath chal sakte hain. Har tyohaar mein koi na koi ganit chhupa hai, dhoondho! 🎉

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🟢 Master Recap

Rhombus diagonals: aadha + 90°.
Area = ½ × d₁ × d₂.
Bahar ke rectangle ka aadha.
Kite aur square pe bhi; rectangle pe nahi.
Side = √((d₁/2)² + (d₂/2)²).

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👉 Aage Kya?

Ab ek jodi parallel sides wala: trapezium. Do copies jodo, parallelogram ban jaata! ⏢

← Pichla: Post 5 — Parallelogram Ka Area 📚 Chapter 7 ke saare posts Agla: Post 7 — Trapezium Ka Area →

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✅ Pehle Yeh Aata Hai?

🎬 Kahani: Patang Ka Kaagaz

📖 Concept: Area = ½ × d₁ × d₂

Step 1: Diagonals 90° pe

Step 2: Do triangles se

Step 3: Bahar ka rectangle

Step 4: Base × height bhi chalega

Step 5: Side bhi diagonals se

🔐 Deep Concept: Kite Ka Bhi Yahi Formula

✏️ 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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