Triangle Ka Area | Class 8 Maths Book 2 Ch 7

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

Triangle 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:

8 × 5 = ?
Rectangle 8 × 5 ka aadha?
Height (oonchaai) base ke saath kitne degree pe?

Answers dekho

40
20
90°

Teeno sahi? Badhiya! Rectangle wala post: Post 1.

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🎬 Kahani: Samose Ki Tikoni Plate

Rohan ko ek tikoni (triangle) plate ka area chahiye tha, uspe sajaavat ka kaagaz lagaana tha. Unit squares gine to kinaaron pe aadhe-adhoore squares!

Priya boli, “Triangle ko ek rectangle ke andar rakh ke dekho. Kitna hissa gherta hai?” Rohan ne dekha… bilkul aadha! 🔺

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📖 Concept: Area = ½ × Base × Height

Step 1: Diagonal wala triangle

Rectangle (b × h) ka diagonal = 2 barabar triangles. Ek triangle = ½ × b × h.

Step 2: Kisi bhi triangle ko rectangle mein

Baayein: triangle rectangle mein. Daayein: bahar ki taraf height (obtuse).

Upar ke kone se base pe seedhi (90°) line = height h. Yeh triangle ko do right triangles mein baantti hai. Har right triangle apne chhote rectangle ka aadha. Jodo: triangle = aadha bada rectangle = ½ × b × h.

WHY har triangle? Har triangle ko height se do right triangles mein toda ja sakta hai.

Step 3: Height bahar ho to bhi

Obtuse triangle (ek kona 90° se bada): height base ki badhaai hui line pe girti hai. Bada right triangle − chhota right triangle = ½(b + x)h − ½xh = ½ × b × h. Formula phir bhi wahi!

Step 4: Koi bhi side base

Teeno sides mein se koi bhi base ho sakti, bas uski height (saamne ke kone se us side pe 90°) lo. Teeno ka area ek hi aayega.

Step 5: Udaharan

Base 5 cm, height 3.2 cm → ½ × 5 × 3.2 = 8 cm². Right triangle 3, 4 → ½ × 3 × 4 = 6 cm².

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🔐 Deep Concept: Ek Triangle, Teen Base, Ek Area

Area = ½ × a × hₐ = ½ × b × h_b = ½ × c × h_c. To a × hₐ = b × h_b! Lambi side ki height chhoti, chhoti side ki height lambi.

Isse ek height se doosri nikal sakte ho (agla post). Jaise sides 6 aur 8, 6 wali side ki height 4: area 12, to 8 wali side ki height = 24 ÷ 8 = 3. 🔐

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✏️ Solved Examples

Example 1 (Easy): Right triangle, legs 3 cm, 4 cm. Area?

½ × 3 × 4 = 6 cm².

WHY sahi hai? 3 × 4 rectangle (12) ka aadha ✅

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Example 2 (Medium): Base 5 cm, height 3.2 cm?

½ × 5 × 3.2 = 8 cm².

WHY sahi hai? 5 × 3.2 = 16, aadha 8 ✅

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Example 3 (NCERT style): Rectangle 5 × 4 mein XDC triangle, base DC = 5, height 4.

½ × 5 × 4 = 10 sq. units.

WHY sahi hai? Rectangle ka aadha ✅

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Priya ka mantra: “Triangle = aadha rectangle!” 🎉

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🏠 Real Life Mein

🍕 Pizza slice, samose ki tikoni plate.
⛺ Tent ka kapda (tikoni deewar).
🏠 Chhat ki tikoni deewar (paint).
⛵ Naav ki paal (sail).

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🧭 Kab Use Karein, Kab Nahi

Situation	Kya karein	Kyun
Kisi bhi triangle	✅ ½ × b × h	Hamesha
Height = side lambaai (right triangle)	✅ Legs ka guna ÷ 2	90° wale
Tirchhi side ko height	❌ Galat	Height 90° pe
Obtuse	✅ Height bahar	Base badhaao

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❌→✅ Worked Mistake

Sawaal: Triangle sides 5, 5, 6 (isosceles). Area?

❌ Galat: “½ × 6 × 5 = 15.”

Galti kya hai? 5 tirchhi side hai, height nahi ❌

✅ Sahi: Height 6 ko aadha karti: √(25 − 9) = 4. Area = ½ × 6 × 4 = 12.

Yaad rakho: Height = base pe 90° (Ch 2 ka theorem se).

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📝 10 MCQs

Q1. Triangle area?

(a) ½ × b × h

(b) b × h

(c) b + h

(d) 2bh

Solution dekho

Sahi jawab: (a)

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

Q2. Legs 3, 4?

(a) 6

(b) 12

(c) 7

(d) 5

Solution dekho

Sahi jawab: (a)

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

Q3. Base 5, h 3.2?

(a) 8

(b) 16

(c) 8.2

(d) 4

Solution dekho

Sahi jawab: (a)

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

Q4. Height kya?

(a) Saamne kone se base pe 90°

(b) Koi bhi side

(c) Lambi side

(d) Diagonal

Solution dekho

Sahi jawab: (a)

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

Q5. Obtuse mein height?

(a) Base ke bahar gir sakti

(b) Hoti nahi

(c) Hamesha andar

(d) Side

Solution dekho

Sahi jawab: (a)

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

Q6. Sides 5, 5, 6 area?

(a) 12

(b) 15

(c) 30

(d) 24

Solution dekho

Sahi jawab: (a)

(a) sahi: h = 4 ✅
(b) galat: Galat height.
(c) galat: Nahi.
(d) galat: Nahi.

Q7. Kya base badalne se area badalta?

(a) Nahi

(b) Haan

(c) Kabhi

(d) Double

Solution dekho

Sahi jawab: (a)

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

Q8. a × hₐ = ?

(a) b × h_b

(b) a + b

(c) hₐ + h_b

(d) a ÷ hₐ

Solution dekho

Sahi jawab: (a)

(a) sahi: Dono 2 × area ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

Q9. Rectangle 8 × 6 ka diagonal triangle?

(a) 24

(b) 48

(c) 14

(d) 28

Solution dekho

Sahi jawab: (a)

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

Q10. Base 10, area 25, height?

(a) 5

(b) 2.5

(c) 10

(d) 50

Solution dekho

Sahi jawab: (a)

(a) sahi: 2 × 25 ÷ 10 ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

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❓ FAQs (Bachchon Ke Asli Sawaal)

1. ½ kyun?

Triangle aadha rectangle.

2. Height kaise naapein?

Set square se base pe 90° line.

3. Equilateral triangle?

Height √(a² − (a/2)²) (Ch 2).

4. Teeno heights kahan milti?

Ek point pe (orthocentre), aage padhoge.

5. Units?

cm², m².

6. Kya ½ × b × h har triangle pe?

Haan, hamesha.

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🏋️ Practice Zone (12 Sawaal)

Q1. Easy Base 10, h 6?

Solution dekho

30.

Q2. Easy Legs 5, 12?

Solution dekho

30.

Q3. Easy Base 7, h 4?

Solution dekho

14.

Q4. Easy Area 20, base 8. h?

Solution dekho

Q5. Medium Equilateral side 6 (h ≈ 5.2). Area?

Solution dekho

≈ 15.6.

Q6. Medium Sides 10, 10, 12. Area?

Solution dekho

h = 8 → 48.

Q7. Medium Base 4 cm, h 4.5 cm?

Solution dekho

9 cm².

Q8. NCERT style 3 cm, 4 cm right triangle aur 5 cm, 3.2 cm triangle ke area.

Solution dekho

6 aur 8 cm².

Q9. NCERT style Obtuse triangle ka formula kyun same?

Solution dekho

Bada − chhota right triangle.

Q10. Medium Sides 6, 8, 10 (right). 10 pe height?

Solution dekho

Area 24 → 4.8.

Q11. Medium Base double, height aadhi. Area?

Solution dekho

Same.

Q12. NCERT style Rectangle ko triangle mein badlo, area same (Śulba).

Solution dekho

Base double, height same, ya base same, height double.

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🧠 HOTS (Sochne Wale Sawaal)

Q1. Base same, height same, alag shape ke triangles?

Solution dekho

Area barabar!

Q2. Triangle ka base 20% badha, height 20% ghati. Area?

Solution dekho

1.2 × 0.8 = 0.96 → 4% ghata.

Q3. Kya do alag triangles same area, alag perimeter?

Solution dekho

Haan.

Q4. Square (side 6) ke kone se kone triangle?

Solution dekho

18.

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🏆 Olympiad Corner

Q1. Triangle 13, 14, 15 (14 base, h 12). Area?

Solution dekho

84.

Q2. Usi ka 13 wali side ki height?

Solution dekho

168 ÷ 13 ≈ 12.92.

Q3. Isosceles 13, 13, 10?

Solution dekho

h = 12 → 60.

Q4. Right triangle area 30, ek leg 5. Hypotenuse?

Solution dekho

Doosra leg 12 → 13.

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💗 CharuMam Motivation

Rohan ne triangle ko rectangle mein rakha, aur mushkil aasaan ho gayi. 🔺

Naye sawaal ko kisi purane, jaane-pehchaane sawaal se jodo. Yahi seekhne ki asli chaabi hai! 🔑

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🟢 Master Recap

Triangle = ½ × base × height.
Height = saamne kone se base pe 90°.
Har triangle (obtuse bhi) pe chalta.
Koi bhi side base; area same.
a × hₐ = b × h_b.

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👉 Aage Kya?

Formula ke kamaal: gumshuda height, median ka jaadu, diagonals ke 4 triangles! Agle post mein. ✨

← Pichla: Post 1 — Rectangle Aur Square Ka Area 📚 Chapter 7 ke saare posts Agla: Post 3 — Triangle Area Ke Kamaal →

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

✅ Pehle Yeh Aata Hai?

🎬 Kahani: Samose Ki Tikoni Plate

📖 Concept: Area = ½ × Base × Height

Step 1: Diagonal wala triangle

Step 2: Kisi bhi triangle ko rectangle mein

Step 3: Height bahar ho to bhi

Step 4: Koi bhi side base

Step 5: Udaharan

🔐 Deep Concept: Ek Triangle, Teen Base, Ek 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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