Dosto, Mensuration 2D matlab flat (chapti) aakritiyon ka ganit — square, rectangle, triangle, circle waghairah ka Area (kshetrafal) aur Perimeter (parimap).
CET Group D mein isse 1–2 questions aate hain aur ye sabse aasan marks hain — kyunki sawal seedha formula par hote hain. Formula yaad hai to 20 second mein answer, nahi yaad to sawal chhodna padega. Bas itni si baat!
Do shabd clear kar lo: Area = andar ki jagah (unit hamesha square: cm², m²) aur Perimeter = charon taraf ki lambai (unit normal: cm, m). Chalo formulas ratt lete hain! 💪
1. Square (Varg) aur Rectangle (Aayat)
| Aakriti | Area | Perimeter | Diagonal (vikarn) |
|---|---|---|---|
| Square (bhuja a) | a² | 4a | a√2 |
| Rectangle (l × b) | l × b | 2(l + b) | √(l² + b²) |
Step 2: Perimeter = 4 × 14 = 56 cm ✓ (pehle bhuja nikalo, phir jo poocha hai wo)
2. Triangle (Tribhuj)
| Kis type ka | Area formula |
|---|---|
| Koi bhi triangle (base & height pata ho) | ½ × base × height |
| Teeno bhujaayein pata hon (Heron) | √[s(s−a)(s−b)(s−c)], jahan s = (a+b+c)/2 |
| Equilateral (sab bhuja a) | (√3/4) a² · height = (√3/2) a |
| Right-angled | ½ × dono chhoti bhujaon ka guna · Pythagoras: h² = p² + b² |
Equilateral side 4 cm ka area = (√3/4) × 16 = 4√3 ≈ 6.93 cm²
3. Parallelogram, Rhombus & Trapezium
| Aakriti | Area | Khas baat |
|---|---|---|
| Parallelogram | base × height | Aamne-saamne bhuja barabar & samanantar |
| Rhombus (samchaturbhuj) | ½ × d₁ × d₂ | Charon bhuja barabar; diagonals 90° par kaatte hain |
| Trapezium (samlamb) | ½ × (a + b) × h | a, b = samanantar bhujaayein |
Trapezium: samanantar bhuja 12 aur 8 cm, height 5 cm → ½ × 20 × 5 = 50 cm²
Parallelogram: base 12, height 7 → 84 cm²
4. Circle (Vritt) — ⭐ Sabse zyada aane wala
| Kya | Formula | π = 22/7 se |
|---|---|---|
| Area | πr² | r = 7 → 154 |
| Circumference (parimap) | 2πr = πd | r = 14 → 88 |
| Semicircle area | ½πr² | Perimeter = πr + 2r |
| Ring (do circle ke beech) | π(R² − r²) | Bada minus chhota |
Step 2: Area = (22/7) × 49 = 154 cm² ✓
5. % Badhne par Area ka Kya Hota Hai (Ch 4 ka jod)
Step 1: 20 + 20 + (20×20)/100 = 44% ✓ (ye Chapter 4 wala successive formula hi hai!)
Check: bhuja 10 → 12; area 100 → 144, yaani 44% ✓
"Rectangle ka area 120, lambai 15 → chaudai?" → 120 ÷ 15 = 8 cm.
Rule: hamesha pehle basic maap (bhuja/radius) nikalo.
Step 1: Unit same karo: kamra 1200 cm × 800 cm = 9,60,000 cm²
Step 2: Ek tile = 1600 cm² → 960000 ÷ 1600 = 600 tiles
"Khet ke charon taraf taar" wale sawal mein perimeter lagta hai, area nahi!
Percentage mein: x% badhe → area 2x + x²/100 % badhega (20% → 44%).
cm² = area · cm = perimeter
Options mein unit dekho — agar cm² likha hai to answer area hai. Aadhe galat options isi se cut jaate hain!
Radius mein 7 → π = 22/7
r = 7, 14, 21 diya ho to 22/7 lo — 7 cancel hokar answer poora number (154, 616, 88) aata hai. Ye numbers exam mein baar-baar aate hain.
½ lagta hai: triangle, rhombus, trapezium
Triangle = ½bh · Rhombus = ½d₁d₂ · Trapezium = ½(a+b)h. Teeno mein ½ — ek saath yaad karo, teeno hamesha yaad rahenge.
3-4-5 · 5-12-13 · 8-15-17 · 7-24-25
Rectangle ka diagonal ya right triangle ka sawal aaye to calculation ki zaroorat hi nahi — 12 aur 5 dikhe to answer 13!
Bhuja ×2 → area ×4
Aur % mein: 2x + x²/100 (Ch 4 ka successive). 10% → 21%, 20% → 44%, 50% → 125%.
| Aakriti | Area | Perimeter / aur |
|---|---|---|
| Square | a² | 4a · diagonal a√2 |
| Rectangle | l×b | 2(l+b) · diagonal √(l²+b²) |
| Triangle | ½bh | Heron: √[s(s−a)(s−b)(s−c)] |
| Equilateral | (√3/4)a² | height (√3/2)a |
| Parallelogram | b × h | 2(a+b) |
| Rhombus | ½d₁d₂ | 4 × bhuja |
| Trapezium | ½(a+b)h | a, b = samanantar |
| Circle | πr² | 2πr |
| Semicircle | ½πr² | πr + 2r |
| Ring | π(R²−r²) | — |
| 1 m² | 10,000 cm² | |
| Bhuja x% badhe | Area 2x + x²/100 % badhe | |
Q1. The area of a square whose side is 12 cm is:
Q2. The perimeter of a rectangle of length 15 cm and breadth 10 cm is:
Q3. The area of a triangle with base 10 cm and height 8 cm is:
Q4. The area of a circle of radius 7 cm is (take π = 22/7):
Q5. The circumference of a circle of radius 14 cm is (take π = 22/7):
Q6. The area of an equilateral triangle of side 4 cm is:
Q7. The area of a rhombus whose diagonals are 16 cm and 12 cm is:
Q8. The area of a trapezium whose parallel sides are 12 cm and 8 cm and height 5 cm is:
Q9. The area of a square is 196 cm². Its perimeter is:
Q10. The area of a rectangle is 120 cm² and its length is 15 cm. Its breadth is:
Q11. The diagonal of a rectangle of length 12 cm and breadth 5 cm is:
Q12. The circumference of a circle is 44 cm. Its radius is (take π = 22/7):
Q13. The area of a parallelogram with base 12 cm and height 7 cm is:
Q14. If the side of a square is increased by 20%, its area increases by:
Ye chapter pure formula-based hai — yaad hai to marks pakke. Square a², 4a; rectangle l×b, 2(l+b); teen "aadhe" wale saath yaad karo — triangle ½bh, rhombus ½d₁d₂, trapezium ½(a+b)h; parallelogram mein ½ nahi lagta. Circle: πr² aur 2πr, aur radius mein 7 dikhe to π = 22/7 lo (r=7 → area 154, r=14 → circumference 88). Diagonal ke liye Pythagoras triplets (5-12-13) ratt lo. Aur maap x% badhe to area 2x + x²/100 % badhta hai — bhuja dugni hone par area 4 guna! 🚀