Maths-5 Area based Practice Questions and Step-by-Step Solutions for Competitive Exams SSC, BSSC, Bank,Railways)

Maths-5 Area based practice Questions and Step-by-Step Solutions for Competitive Exams SSC, BSSC, Bank,Railways)

A Set of 20 area based practice questions with step-by-step solutions, covering all major 2D shapes. These will help you master geometry for CDS, SSC, UPSC, and other exams.

Area Based Practice Questions with Step-by-Step Solutions

🔹 1. Area of a Square

Q: Find the area of a square with side 9 cm.
Solution:
Area = side × side = ( 9 × 9 = 81 ) cm² ✅

🔹 2. Area of a Rectangle

Q: Length = 12 cm, Breadth = 5 cm
Solution:
Area = ( 12 × 5 = 60 ) cm² ✅

🔹 3. Area of a Triangle

Q: Base = 10 cm, Height = 6 cm
Solution:
Area = 1/2 × 10 × 6 = 30 ) cm² ✅

🔹 4. Area of a Circle

Q: Radius = 7 cm
Solution:
Area = π × r^2 = 22/7 × 7 × 7 = 154 ) cm² ✅

🔹 5. Area of a Parallelogram

Q: Base = 15 cm, Height = 8 cm
Solution:
Area = ( 15 × 8 = 120 ) cm² ✅

🔹 6. Area of a Trapezium

Q: Parallel sides = 10 cm and 6 cm, Height = 4 cm
Solution:
Area = 1/2 × (10 + 6) × 4 = 32 ) cm² ✅

🔹 7. Area of a Rhombus

Q: Diagonals = 12 cm and 16 cm
Solution:
Area = 1/2 × 12 × 16 = 96 ) cm² ✅

🔹 8. Area of an Equilateral Triangle

Q: Side = 6 cm
Solution:
Area = sqrt3/4 × a^2 = sqrt 3 / 4 × 36 ≈ 15.59 ) cm² ✅

🔹 9. Area of a Semi-Circle

Q: Radius = 14 cm
Solution:
Area = 1/ 2 × π × r^2 = 1/2 × 22/7 × 14 × 14 = 308 ) cm² ✅

🔹 10. Area of a Right-Angled Triangle

Q: Base = 9 cm, Height = 12 cm
Solution:
Area = 1/ 2 × 9 × 12 = 54 ) cm² ✅

🔹 11. Area of a Square Field

Q: Side = 25 m
Solution:
Area = ( 25 × 25 = 625 ) m² ✅

🔹 12. Area of a Rectangular Garden

Q: Length = 30 m, Breadth = 20 m
Solution:
Area = ( 30 × 20 = 600 ) m² ✅

🔹 13. Area of a Circular Pond

Q: Radius = 10 m
Solution:
Area = ( π × r^2 = 3.14 × 100 = 314 ) m² ✅

🔹 14. Area of a Triangle with sides 13 cm, 14 cm, 15 cm (Heron’s Formula)

Solution:
s = (13 + 14 + 15) / 2 = 21
Area = sqrt{21(21-13)(21-14)(21-15)} = sqrt{21 × 8 × 7 × 6} = sqrt 7056 ≈ 84 ) cm² ✅

🔹 15. Area of a Path Around a Square

Q: Outer square side = 10 m, inner square side = 8 m
Solution:
Area = ( 10^{2 –} 8^2 = 100 – 64 = 36 ) m² ✅

🔹 16. Area of a Path Around a Rectangle

Q: Outer = 20 × 15 m, Inner = 18 × 13 m
Solution:
Area = ( (20 × 15) – (18 × 13) = 300 – 234 = 66 ) m² ✅

🔹 17. Area of a Sector of Circle

Q: Radius = 7 cm, Angle = 90°
Solution:
Area = θ/360 × π × r^2 = 90°/{360} × 22/7 × 49 = 94.5 ) cm² ✅

🔹 18. Area of a Shaded Region (Circle inside Square)

Q: Square side = 14 cm, Circle radius = 7 cm
Solution:
Area = ( 14^{2 – π X} 7^2 = 196 – 154 = 42 ) cm² ✅

🔹 19. Area of a Composite Shape (Rectangle + Triangle)

Q: Rectangle = 10 × 6 cm, Triangle base = 10 cm, height = 4 cm
Solution:
Area = ( (10 × 6) + 1/2 × 10 × 4 = 60 + 20 = 80 ) cm² ✅

🔹 20. Area of a Circle from Diameter

Q: Diameter = 28 cm → Radius = 14 cm
Solution:
Area = ( π × 14^2 = 22/7 × 196 = 616 ) cm² ✅