📑 Topics on this page (Jump to Topic):
📌 1. Formula Table
| Figure | Area | Perimeter |
|---|---|---|
| Rectangle | l × b | 2(l + b) |
| Square | a² = d²/2 | 4a |
| Triangle | ½ × base × height; Heron √[s(s−a)(s−b)(s−c)] | a + b + c |
| Equilateral triangle | (√3/4)a² | 3a |
| Rhombus | ½ d₁d₂ | 4a |
| Trapezium | ½ × (sum of parallel sides) × height | — |
| Circle | πr² | 2πr |
| Sector (θ) | (θ/360)πr² | (θ/360)2πr + 2r |
| Ring | π(R² − r²) | — |
- Rhombus: a² = (d₁/2)² + (d₂/2)².
- Diagonal of rectangle = √(l² + b²).
⚠️ Exam Traps:
- When a side increases by x%, area increases by (2x + x²/100)%, not x%.
- Use π = 22/7 when the radius is a multiple of 7.
📌 2. Practice MCQs
📝 Practice MCQs (prepared by SF Prep — not PYQs)
Q1. The area of a circle of radius 21 cm is (π = 22/7): Practice
Correct answer: (B)
Solution: πr² = 22/7 × 21² = 1386 cm².
Solution: πr² = 22/7 × 21² = 1386 cm².
Q2. The area of a triangle with sides 7 cm, 15 cm and 20 cm is: Practice
Correct answer: (C)
Solution: s = 21; √[21×14×6×1] = 42 cm².
Solution: s = 21; √[21×14×6×1] = 42 cm².
Q3. The diagonals of a rhombus are 18 cm and 24 cm. Its perimeter is: Practice
Correct answer: (D)
Solution: Side = √(9² + 12²) = 15; perimeter = 4 × 15 = 60 cm.
Solution: Side = √(9² + 12²) = 15; perimeter = 4 × 15 = 60 cm.
Q4. If the side of a square is increased by 20%, by what percent does its area increase? Practice
Correct answer: (A)
Solution: 2x + x²/100 = 40 + 4 = 44%.
Solution: 2x + x²/100 = 40 + 4 = 44%.
Q5. A rectangle has length 24 m and diagonal 25 m. Its area is: Practice
Correct answer: (B)
Solution: Breadth = √(25² − 24²) = 7; area = 24 × 7 = 168 m².
Solution: Breadth = √(25² − 24²) = 7; area = 24 × 7 = 168 m².
Q6. The area of an equilateral triangle of side 8√3 cm is: Practice
Correct answer: (C)
Solution: (√3/4) × (8√3)² = (√3/4) × 192 = 48√3 cm².
Solution: (√3/4) × (8√3)² = (√3/4) × 192 = 48√3 cm².
Q7. The area of a sector of angle 45° in a circle of radius 7 cm is (π = 22/7): Practice
Correct answer: (D)
Solution: (θ/360)πr² = (45/360) × 22/7 × 49 = 19.25 cm².
Solution: (θ/360)πr² = (45/360) × 22/7 × 49 = 19.25 cm².
Q8. A trapezium has parallel sides 14 cm and 25 cm, 10 cm apart. Its area is: Practice
Correct answer: (A)
Solution: ½ × (14 + 25) × 10 = 195 cm².
Solution: ½ × (14 + 25) × 10 = 195 cm².
Q9. The area of a circle of radius 3.5 cm is (π = 22/7): Practice
Correct answer: (B)
Solution: πr² = 22/7 × 3.5² = 38.5 cm².
Solution: πr² = 22/7 × 3.5² = 38.5 cm².
Q10. The area of a triangle with sides 5 cm, 12 cm and 13 cm is: Practice
Correct answer: (C)
Solution: s = 15; √[15×10×3×2] = 30 cm².
Solution: s = 15; √[15×10×3×2] = 30 cm².
Q11. The diagonals of a rhombus are 16 cm and 30 cm. Its perimeter is: Practice
Correct answer: (D)
Solution: Side = √(8² + 15²) = 17; perimeter = 4 × 17 = 68 cm.
Solution: Side = √(8² + 15²) = 17; perimeter = 4 × 17 = 68 cm.
Q12. A rectangle has length 15 m and diagonal 17 m. Its area is: Practice
Correct answer: (A)
Solution: Breadth = √(17² − 15²) = 8; area = 15 × 8 = 120 m².
Solution: Breadth = √(17² − 15²) = 8; area = 15 × 8 = 120 m².
Q13. The area of an equilateral triangle of side 12√3 cm is: Practice
Correct answer: (B)
Solution: (√3/4) × (12√3)² = (√3/4) × 432 = 108√3 cm².
Solution: (√3/4) × (12√3)² = (√3/4) × 432 = 108√3 cm².
Q14. The area of a sector of angle 60° in a circle of radius 21 cm is (π = 22/7): Practice
Correct answer: (C)
Solution: (θ/360)πr² = (60/360) × 22/7 × 441 = 231 cm².
Solution: (θ/360)πr² = (60/360) × 22/7 × 441 = 231 cm².
Q15. The area of a circle of radius 14 cm is (π = 22/7): Practice
Correct answer: (D)
Solution: πr² = 22/7 × 14² = 616 cm².
Solution: πr² = 22/7 × 14² = 616 cm².
Q16. The area of a triangle with sides 13 cm, 14 cm and 15 cm is: Practice
Correct answer: (A)
Solution: s = 21; √[21×8×7×6] = 84 cm².
Solution: s = 21; √[21×8×7×6] = 84 cm².
Q17. The diagonals of a rhombus are 14 cm and 48 cm. Its perimeter is: Practice
Correct answer: (B)
Solution: Side = √(7² + 24²) = 25; perimeter = 4 × 25 = 100 cm.
Solution: Side = √(7² + 24²) = 25; perimeter = 4 × 25 = 100 cm.
Q18. If the side of a square is increased by 25%, by what percent does its area increase? Practice
Correct answer: (C)
Solution: 2x + x²/100 = 50 + 6.25 = 56.25%.
Solution: 2x + x²/100 = 50 + 6.25 = 56.25%.
Q19. A rectangle has length 40 m and diagonal 41 m. Its area is: Practice
Correct answer: (D)
Solution: Breadth = √(41² − 40²) = 9; area = 40 × 9 = 360 m².
Solution: Breadth = √(41² − 40²) = 9; area = 40 × 9 = 360 m².
Q20. The area of an equilateral triangle of side 10√3 cm is: Practice
Correct answer: (A)
Solution: (√3/4) × (10√3)² = (√3/4) × 300 = 75√3 cm².
Solution: (√3/4) × (10√3)² = (√3/4) × 300 = 75√3 cm².