Parallelogram Ka Area | Class 8 Maths Book 2 Ch 7

📘 Class 8 · Ganita Prakash Book 2Ch 7 · AreaPost 5 / 8⏱ 25–30 min

Parallelogram 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:

Parallelogram ki aamne-saamne sides kaisi?
5 × 4.8 = ?
RHS congruence kya hai?

Answers dekho

Barabar aur parallel
24
Right angle, hypotenuse, ek side barabar

Teeno sahi? Badhiya! Polygon wala: Post 4.

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🎬 Kahani: Tircha Chocolate Bar

Golu ke paas ek tircha (parallelogram) chocolate bar tha. Rohan ka seedha rectangle. Dono ka base barabar, oonchaai barabar. “Mera bada!” Golu bola.

Priya ne Golu ke bar ka ek tikona kona kaata aur doosri taraf chipkaaya: woh bhi bilkul rectangle ban gaya, Rohan jitna! 🍫

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📖 Concept: Area = Base × Height

Step 1: Kaat ke khiskao

Ek kone ka triangle kaat ke doosri taraf: rectangle b × h.

Parallelogram ABCD mein A se CD pe perpendicular AX. ∆AXD kaat ke doosri taraf (BYC ki jagah) lagao: rectangle ABYX banta, area = b × h. (∆AXD ≅ ∆BYC, RHS se.)

Area = base × height

Step 2: Height ≠ tirchhi side

Height = base pe 90° ki doori. Tirchhi side height se lambi (hypotenuse!).

Step 3: Koi bhi side base

Doosri side ko base lo, uski height lo: area same. a × hₐ = b × h_b.

Step 4: Rectangle vs parallelogram (same sides)

Sides 5 aur 4: rectangle 20. Parallelogram height 4 se kam (tircha), to area 20 se kam. Rectangle jeeta!

Step 5: Triangle se rishta

Diagonal parallelogram ko 2 barabar triangles mein. Triangle = ½ × b × h. Yaani triangle ka double area ka rectangle: base same, height same!

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🔐 Deep Concept: Same Base, Same Height, Same Area

Do parallel lines ke beech, same base pe jitne bhi parallelograms banao (kitne bhi tirchhe), area sab barabar! Par perimeter alag: jitna tircha, utna zyada.

Isliye ek rectangle ko “dhakka” do (upar wali side khiskaao), area wahi, shape badli. Taash ki gaddi ko tircha karo, cards utne hi! 🃏🔐

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✏️ Solved Examples

Example 1 (Easy): Base 7, height 4?

28.

WHY sahi hai? 7 × 4 ✅

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Example 2 (Medium): Sides 12 aur 7.6, 12 pe height 6. 7.6 pe height (QN)?

Area 72 → 72 ÷ 7.6 ≈ 9.47 cm.

WHY sahi hai? Area same ✅

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Example 3 (NCERT style): Rectangle aur parallelogram, sides 5 aur 4. Kaun bada?

Rectangle (20); parallelogram ki height < 4.

WHY sahi hai? Same base pe banao ✅

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Priya ka mantra: “Tircha karo, area wahi; height dekho!” 🎉

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🏠 Real Life Mein

🃏 Taash ki tirchhi gaddi.
🏗️ Seedhi ki railing, pul ke design.
🌾 Tirchhe khet.
🪟 Kuch khidkiyon ke kaanch.

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🧭 Kab Use Karein, Kab Nahi

Situation	Kya karein	Kyun
Parallelogram	✅ b × h	Kaat-khiskao
Tirchhi side × base	❌ Galat	Height 90°
Doosri height	✅ Area ÷ doosri side	Area same
Same base, parallel lines	✅ Area same	Perimeter alag

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❌→✅ Worked Mistake

Sawaal: Sides 10 aur 6, angle 60°. “Area = 60.”

❌ Galat: Tirchhi side ko height maana ❌

✅ Sahi: Height 6 se kam (≈ 5.2). Area ≈ 52.

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📝 10 MCQs

Q1. Area?

(a) b × h

(b) ½ b h

(c) b + h

(d) tirchhi × base

Solution dekho

Sahi jawab: (a)

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

Q2. Base 7, h 4?

(a) 28

(b) 14

(c) 11

(d) 22

Solution dekho

Sahi jawab: (a)

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

Q3. Kaat ke kya banta?

(a) Rectangle

(b) Triangle

(c) Square hamesha

(d) Circle

Solution dekho

Sahi jawab: (a)

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

Q4. Kaun sa congruence?

(a) RHS

(b) SSS hamesha

(c) AAA

(d) Koi nahi

Solution dekho

Sahi jawab: (a)

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

Q5. Sides 5, 4: bada?

(a) Rectangle

(b) Parallelogram

(c) Barabar

(d) Pata nahi

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Nahi.
(c) galat: Tab tak nahi jab tak tircha.
(d) galat: Nahi.

Q6. Same base, parallel lines ke beech?

(a) Area same

(b) Perimeter same

(c) Dono same

(d) Kuch nahi

Solution dekho

Sahi jawab: (a)

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

Q7. Diagonal se?

(a) 2 barabar triangles

(b) 4 triangles

(c) Rectangle

(d) Kuch nahi

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Dono diagonals se 4.
(c) galat: Nahi.
(d) galat: Nahi.

Q8. Area 72, side 7.6, height?

(a) ≈ 9.47

(b) 72

(c) 6

(d) 12

Solution dekho

Sahi jawab: (a)

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

Q9. Height kya?

(a) Base pe 90° doori

(b) Tirchhi side

(c) Diagonal

(d) Base

Solution dekho

Sahi jawab: (a)

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

Q10. Base 4.4, h 2?

(a) 8.8

(b) 6.4

(c) 4.4

(d) 17.6

Solution dekho

Sahi jawab: (a)

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

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❓ FAQs (Bachchon Ke Asli Sawaal)

1. Rectangle bhi parallelogram?

Haan, 90° wala.

2. Triangle double?

Same base-height ka parallelogram = 2 × triangle.

3. Height bahar gire?

Base badhao; formula wahi.

4. Perimeter?

2(a + b), area se alag.

5. Rhombus?

Parallelogram hai; agla post.

6. Śulba-Sūtra?

Triangle ko rectangle mein badalne ke tareeke (base aadha ya height aadhi).

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🏋️ Practice Zone (12 Sawaal)

Q1. Easy Base 9, h 5?

Solution dekho

45.

Q2. Easy Area 60, base 12. h?

Solution dekho

Q3. Easy Base 4, h 7?

Solution dekho

28.

Q4. Easy Base 5, h 4.8?

Solution dekho

24.

Q5. Medium Sides 10, 8; 10 pe h 6. 8 pe h?

Solution dekho

60 ÷ 8 = 7.5.

Q6. Medium Triangle (b 6, h 4) ka double rectangle?

Solution dekho

6 × 4 = 24.

Q7. Medium Base 3, h 5 aur base 5, h 3?

Solution dekho

Dono 15.

Q8. NCERT style Kaat-khiskao se formula samjhao.

Solution dekho

∆ kaat ke doosri taraf → rectangle b × h.

Q9. NCERT style Rectangle vs parallelogram (5, 4)?

Solution dekho

Rectangle bada.

Q10. Medium Square side 6 ko tircha (h 5) kiya. Area?

Solution dekho

30.

Q11. Medium Equilateral triangle aur square (same side 4): kaun bada?

Solution dekho

Square 16; triangle ≈ 6.9.

Q12. NCERT style Do equilateral triangles + square (side same)?

Solution dekho

2 × 0.43a² + a² ≈ 1.87a².

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🧠 HOTS (Sochne Wale Sawaal)

Q1. Parallelogram ka area 0 kab?

Solution dekho

Jab bilkul chapta (height 0).

Q2. Sides fixed (5, 4), area sabse zyada kab?

Solution dekho

Rectangle (90°).

Q3. Triangle ko rectangle mein (Śulba)?

Solution dekho

Height ke midpoint se kaat ke kone ghumao.

Q4. Kya parallelogram ke 4 triangles (diagonals se) barabar area?

Solution dekho

Haan.

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🏆 Olympiad Corner

Q1. Sides 8, 6, area 24. Angle?

Solution dekho

8 × h = 24 → h = 3 = 6 ka aadha → 30° (ya 150°).

Q2. Area 48, ek height 6, doosri 4. Sides?

Solution dekho

8 aur 12.

Q3. Rectangle 6 × 4 ko “dhakka” do, perimeter 24 ho jaaye?

Solution dekho

Side 4 → 6, height 4 same → area 24 same.

Q4. Do parallelograms same base 10, heights 3 aur 5. Areas?

Solution dekho

30 aur 50.

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💗 CharuMam Motivation

Golu ka tircha bar bhi utna hi bada nikla jitna Rohan ka seedha. 🍫

Alag dikhna kam hona nahi hai. Har kisi ki apni shape, apni taakat! 🌈

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🟢 Master Recap

Parallelogram = base × height.
Kaat-khiskao: rectangle (RHS).
Height = 90° doori, tirchhi side nahi.
Same base + parallel lines = same area.
Same sides mein rectangle sabse bada.

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👉 Aage Kya?

Saari sides barabar parallelogram: rhombus. Iska area diagonals se! 💎

← Pichla: Post 4 — Kisi Bhi Polygon Ka Area 📚 Chapter 7 ke saare posts Agla: Post 6 — Rhombus Ka Area →

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

✅ Pehle Yeh Aata Hai?

🎬 Kahani: Tircha Chocolate Bar

📖 Concept: Area = Base × Height

Step 1: Kaat ke khiskao

Step 2: Height ≠ tirchhi side

Step 3: Koi bhi side base

Step 4: Rectangle vs parallelogram (same sides)

Step 5: Triangle se rishta

🔐 Deep Concept: Same Base, Same Height, Same Area

✏️ 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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