Mensuration
🔶 2D Shapes
1. Square
• Area = side²
• Perimeter = 4 × side
Example:
Q. What is the area of a square whose side is 8 cm?
Options:
A) 64 cm²
B) 16 cm²
C) 32 cm²
D) 24 cm²
Answer: A
Solution: Area = 8² = 64 cm²
2. Rectangle
• Area = length × breadth
• Perimeter = 2(length + breadth)
Example:
Q. A rectangle has length 10 cm and breadth 5 cm. What is its perimeter?
Options:
A) 15 cm
B) 30 cm
C) 50 cm
D) 25 cm
Answer: B
Solution: 2 × (10 + 5) = 30 cm
3. Triangle
• Area = ½ × base × height
Example:
Q. What is the area of a triangle with base 12 cm and height 6 cm?
Options:
A) 72 cm²
B) 36 cm²
C) 48 cm²
D) 60 cm²
Answer: B
Solution: ½ × 12 × 6 = 36 cm²
4. Circle
• Area = πr²
• Circumference = 2πr
Example:
Q. Find the circumference of a circle with radius 7 cm.
Options:
A) 44 cm
B) 22 cm
C) 88 cm
D) 66 cm
Answer: A
Solution: 2 × 22/7 × 7 = 44 cm
5. Parallelogram
• Area = base × height
Example:
Q. A parallelogram has base 9 cm and height 5 cm. What is the area?
Options:
A) 45 cm²
B) 40 cm²
C) 36 cm²
D) 50 cm²
Answer: A
Solution: 9 × 5 = 45 cm²
6. Trapezium
• Area = ½ × (a + b) × height
Example:
Q. Find the area of a trapezium with a = 6 cm, b = 10 cm, height = 4 cm.
Options:
A) 64 cm²
B) 40 cm²
C) 32 cm²
D) 16 cm²
Answer: C
Solution: ½ × (6 + 10) × 4 = 32 cm²
🧊 3D Shapes
7. Cube
• Volume = side³
• Surface Area = 6a²
• Lateral Surface Area = 4a²
Example:
Q. What is the volume of a cube with side 5 cm?
Options:
A) 125 cm³
B) 25 cm³
C) 50 cm³
D) 150 cm³
Answer: A
Solution: 5³ = 125 cm³
8. Cuboid
• Volume = l × b × h
• Surface Area = 2(lb + bh + hl)
Example:
Q. Find the volume of a cuboid with l = 8 cm, b = 3 cm, h = 2 cm.
Options:
A) 48 cm³
B) 24 cm³
C) 32 cm³
D) 36 cm³
Answer: A
Solution: 8 × 3 × 2 = 48 cm³
9. Cylinder
• Volume = πr²h
• CSA = 2πrh
• TSA = 2πr(r + h)
Example:
Q. A cylinder has radius 3 cm and height 7 cm. What is its volume?
Options:
A) 198 cm³
B) 154 cm³
C) 126 cm³
D) 66 cm³
Answer: A
Solution: π × 3² × 7 = 3.14 × 9 × 7 = 198 cm³
10. Cone
• Volume = ⅓πr²h
• CSA = πrl
• TSA = πr(l + r)
Example:
Q. What is the volume of a cone with r = 3 cm and h = 9 cm?
Options:
A) 84.78 cm³
B) 76.3 cm³
C) 90 cm³
D) 99 cm³
Answer: B
Solution: ⅓ × 3.14 × 9 × 9 = 76.3 cm³
🟩 Model Questions with Detailed Solutions
Q1. The area of a square field is 144 m². What is its perimeter?
A) 44 m
B) 48 m
C) 50 m
D) 60 m
✅ Answer: B
📘 Solution: Side = √144 = 12 m, Perimeter = 4 × 12 = 48 m
Q2. A rectangle is 15 m long and 10 m wide. What is its area?
A) 150 m²
B) 250 m²
C) 120 m²
D) 100 m²
✅ Answer: A
📘 Solution: Area = 15 × 10 = 150 m²
Q3. A triangle has base 20 cm and height 10 cm. Find its area.
A) 100 cm²
B) 200 cm²
C) 120 cm²
D) 80 cm²
✅ Answer: A
📘 Solution: Area = ½ × 20 × 10 = 100 cm²
Q4. The circumference of a circle is 44 cm. Find the radius.
A) 7 cm
B) 5 cm
C) 6 cm
D) 8 cm
✅ Answer: A
📘 Solution: 2πr = 44 → r = 44 / (2 × 22/7) = 7 cm
Q5. What is the area of a parallelogram with base 8 cm and height 6 cm?
A) 48 cm²
B) 54 cm²
C) 36 cm²
D) 42 cm²
✅ Answer: A
📘 Solution: Area = 8 × 6 = 48 cm²
Q6. Find the volume of a cube whose side is 4 cm.
A) 64 cm³
B) 16 cm³
C) 32 cm³
D) 48 cm³
✅ Answer: A
📘 Solution: Volume = 4³ = 64 cm³
Q7. A cuboid has dimensions 6 cm × 4 cm × 5 cm. Find the volume.
A) 120 cm³
B) 100 cm³
C) 110 cm³
D) 90 cm³
✅ Answer: A
📘 Solution: Volume = 6 × 4 × 5 = 120 cm³
Q8. A trapezium has bases 8 cm and 12 cm, height 5 cm. What is the area?
A) 50 cm²
B) 60 cm²
C) 45 cm²
D) 55 cm²
✅ Answer: B
📘 Solution: Area = ½ × (8 + 12) × 5 = 50 cm²
Q9. What is the TSA of a cube of side 6 cm?
A) 216 cm²
B) 144 cm²
C) 96 cm²
D) 180 cm²
✅ Answer: A
📘 Solution: TSA = 6 × a² = 6 × 36 = 216 cm²
Q10. Find the CSA of a cylinder with r = 5 cm and h = 10 cm.
A) 314 cm²
B) 440 cm²
C) 628 cm²
D) 220 cm²
✅ Answer: C
📘 Solution: CSA = 2 × π × r × h = 2 × 3.14 × 5 × 10 = 314 × 2 = 628 cm²
