Maths-5 Area: Practice with Tricky Questions and Step-by-Step Solutions for Competitive Exams SSC, BSSC, Bank,Railways

Maths-5 Area: Practice with Tricky Questions and Step-by-Step Solutions for Competitive Exams SSC, BSSC, Bank,Railways

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 ✅

Set of tricky Questions and exam-style area questions with step-by-step solutions, just like those asked in CDS, SSC, UPSC, and other competitive exams. These go beyond direct formula application and test your reasoning, visualization, and composite shape handling.

Tricky Questions with Step-by-Step Solutions

🔹 1. Square Inside a Circle

Q: A square is inscribed in a circle of radius 7 cm. Find the area of the square.

Step 1: Diagonal of square = diameter of circle = 2 × 7 = 14 cm
Step 2: Area of Square= (Diagonal^2)/2

Step 3: Area of Square = 14^2/2  ≈ 98  cm² ✅

🔹 2. Circle Inside a Square

Q: A circle is inscribed in a square of side 14 cm. Find the area of the shaded region (square – circle).

Step 1:

• Area of square = ( 14^2 = 196 ) cm²
• Radius of circle = 7 cm → Area = ( π × 7^2 = 154 ) cm²
  Step 2:
• Shaded area = 196 – 154 = 42 cm² ✅

🔹 3. Path Around a Rectangle

Q: A rectangular garden is 20 m × 15 m. A path 1 m wide is built around it. Find the area of the path.

Step 1:

• Outer rectangle = (20 + 2) × (15 + 2) = 22 × 17 = 374 m²
• Inner rectangle = 20 × 15 = 300 m²
  Step 2:
• Area of path = 374 – 300 = 74 m² ✅

🔹 4. Area of Shaded Region (Two Circles)

Q: A small circle of radius 3 cm is cut out from a larger circle of radius 7 cm. Find the area of the remaining part.

Step 1:

• Large circle = ( π × 7^2 = 154 ) cm²
• Small circle = ( π × 3^2 = 28.27 ) cm²
  Step 2:
• Remaining area = 154 – 28.27 = 125.73 cm² ✅

🔹 5. Triangle from Diagonal of Rectangle

Q: A rectangle has length 10 cm and breadth 6 cm. Find the area of triangle formed by one diagonal.

Step 1:

• Area of rectangle = 10 × 6 = 60 cm²
• Diagonal divides it into 2 equal triangles
  Step 2:
• Area of triangle = 60 ÷ 2 = 30 cm² ✅

🔹 6. Area of Sector

Q: Find the area of a sector of a circle with radius 14 cm and angle 60°.

Step 1:

• Area = θ/360} × π × r^2 = 60/360 × 22/7 × 14 × 14
  Step 2:
• Area = 1/6 × 616 = 102.67 ) cm² ✅

🔹 7. Area of Equilateral Triangle

Q: Find the area of an equilateral triangle of side 12 cm.

Step 1:

• Area = sqrt3/4 × a^2 = sqrt3/4 × 144 ≈ 62.35 ) cm² ✅

🔹 8. Area of a Rhombus from Diagonals

Q: Diagonals of a rhombus are 16 cm and 30 cm. Find its area.

Step 1:

• Area = 1/2 × 16 × 30 = 240 ) cm² ✅

🔹 9. Composite Shape (Rectangle + Semi-circle)

Q: A rectangle of 10 × 4 cm has a semicircle on one shorter side. Find total area.

Step 1:

• Rectangle = 10 × 4 = 40 cm²
• Radius of semicircle = 2 cm → Area = 1/2 × π × 2^2 = 6.28 ) cm²
  Step 2:
• Total area = 40 + 6.28 = 46.28 cm² ✅

🔹 10. Area of Trapezium with Diagonals

Q: A trapezium has parallel sides 10 cm and 6 cm, height 5 cm. Find area.

Step 1:

• Area = 1/2 × (10 + 6) × 5 = 40 ) cm² ✅