Area— Concepts, Formulas & Shortcuts
- Rectangle = l × b; square = a²; parallelogram = base × height.
- Triangle = ½ × base × height; equilateral triangle = (√3/4)a².
- Circle = πr²; circumference = 2πr. Use π = 22/7 when the radius is a multiple of 7.
- Trapezium = ½ × (sum of parallel sides) × height.
- Rhombus = ½ × product of the diagonals.
- If length changes by a% and breadth by b%, area changes by a + b + ab/100 percent.
Area Practice Questions with Answers
Attempt each question first, then open the explanation. All 24 questions below are free to read and require no signup.
Q1.The area of a rectangle 15 cm long and 8 cm wide is:
Easy- A23 cm²
- B46 cm²
- C120 cm²
- D150 cm²
Area question 1 of 24+Show Answer & Explanation
Answer: C. 120 cm²
Explanation: Area = l × b = 15 × 8 = 120 cm².
Q2.The area of a circle of radius 7 cm (π = 22/7) is:
Easy- A44 cm²
- B144 cm²
- C154 cm²
- D176 cm²
Area question 2 of 24+Show Answer & Explanation
Answer: C. 154 cm²
Explanation: πr² = 22/7 × 49 = 154 cm².
Q3.The area of a triangle with base 12 cm and height 5 cm is:
Easy- A17 cm²
- B30 cm²
- C34 cm²
- D60 cm²
Area question 3 of 24+Show Answer & Explanation
Answer: B. 30 cm²
Explanation: ½ × 12 × 5 = 30 cm².
Q4.The perimeter of a square is 64 cm. Its area is:
Easy- A128 cm²
- B196 cm²
- C256 cm²
- D324 cm²
Area question 4 of 24+Show Answer & Explanation
Answer: C. 256 cm²
Explanation: Side = 64/4 = 16 cm → area = 16² = 256 cm².
Q5.The area of an equilateral triangle of side 6 cm is:
Moderate- A6√3 cm²
- B9√3 cm²
- C12√3 cm²
- D18√3 cm²
Area question 5 of 24+Show Answer & Explanation
Answer: B. 9√3 cm²
Explanation: (√3/4) × 6² = (√3/4) × 36 = 9√3 ≈ 15.59 cm².
Q6.If the length of a rectangle is increased by 20% and its breadth decreased by 20%, the area:
Moderate- ARemains the same
- BIncreases by 4%
- CDecreases by 4%
- DDecreases by 2%
Area question 6 of 24+Show Answer & Explanation
Answer: C. Decreases by 4%
Explanation: 1.20 × 0.80 = 0.96, so the area falls by 4%.
Q7.The area of a trapezium with parallel sides 10 cm and 14 cm and height 6 cm is:
Moderate- A60 cm²
- B72 cm²
- C84 cm²
- D140 cm²
Area question 7 of 24+Show Answer & Explanation
Answer: B. 72 cm²
Explanation: ½ × (10 + 14) × 6 = ½ × 24 × 6 = 72 cm².
Q8.The circumference of a circle is 44 cm. Its area (π = 22/7) is:
Moderate- A77 cm²
- B144 cm²
- C154 cm²
- D308 cm²
Area question 8 of 24+Show Answer & Explanation
Answer: C. 154 cm²
Explanation: 2πr = 44 → r = 7 cm → area = 22/7 × 49 = 154 cm².
Q9.The area of a square of side 12 cm is:
Easy- A48 cm²
- B96 cm²
- C144 cm²
- D169 cm²
Area question 9 of 24+Show Answer & Explanation
Answer: C. 144 cm²
Explanation: Area = a² = 12² = 144 cm².
Q10.The area of a parallelogram with base 10 cm and height 7 cm is:
Easy- A35 cm²
- B70 cm²
- C80 cm²
- D140 cm²
Area question 10 of 24+Show Answer & Explanation
Answer: B. 70 cm²
Explanation: Area = base × height = 10 × 7 = 70 cm².
Q11.The area of a rhombus with diagonals 12 cm and 16 cm is:
Moderate- A48 cm²
- B96 cm²
- C144 cm²
- D192 cm²
Area question 11 of 24+Show Answer & Explanation
Answer: B. 96 cm²
Explanation: Area = ½ × d₁ × d₂ = ½ × 12 × 16 = 96 cm².
Q12.The perimeter of a rectangle is 40 cm and its length is 12 cm. Its area is:
Moderate- A84 cm²
- B96 cm²
- C108 cm²
- D120 cm²
Area question 12 of 24+Show Answer & Explanation
Answer: B. 96 cm²
Explanation: 2(l + b) = 40 → l + b = 20 → b = 8 → area = 12 × 8 = 96 cm².
Q13.The area of a circle whose diameter is 14 cm (π = 22/7) is:
Easy- A44 cm²
- B88 cm²
- C154 cm²
- D616 cm²
Area question 13 of 24+Show Answer & Explanation
Answer: C. 154 cm²
Explanation: Radius = 7 cm → area = 22/7 × 49 = 154 cm².
Q14.If each side of a square is increased by 10%, its area increases by:
Moderate- A10%
- B20%
- C21%
- D25%
Area question 14 of 24+Show Answer & Explanation
Answer: C. 21%
Explanation: 1.1² = 1.21, so the area rises by 21%.
Q15.The area of a triangle with sides 3 cm, 4 cm and 5 cm is:
Moderate- A6 cm²
- B7.5 cm²
- C10 cm²
- D12 cm²
Area question 15 of 24+Show Answer & Explanation
Answer: A. 6 cm²
Explanation: It is a right triangle (3² + 4² = 5²) → area = ½ × 3 × 4 = 6 cm².
Q16.A rectangular field 60 m by 40 m has a path 2 m wide inside along its boundary. The area of the path is:
Difficult- A376 m²
- B384 m²
- C400 m²
- D416 m²
Area question 16 of 24+Show Answer & Explanation
Answer: B. 384 m²
Explanation: Outer area = 2,400 m². Inner rectangle = 56 × 36 = 2,016 m². Path = 2,400 − 2,016 = 384 m².
Q17.The area of a rectangle 20 m long and 15 m wide is:
Easy- A70 m²
- B150 m²
- C300 m²
- D350 m²
Area question 17 of 24+Show Answer & Explanation
Answer: C. 300 m²
Explanation: 20 × 15 = 300 m².
Q18.The perimeter of a square of side 9 cm is:
Easy- A18 cm
- B27 cm
- C36 cm
- D81 cm
Area question 18 of 24+Show Answer & Explanation
Answer: C. 36 cm
Explanation: A square has four equal sides, so the perimeter is 4 × 9 = 36 cm.
Q19.The area of a triangle with base 20 cm and height 9 cm is:
Easy- A60 cm²
- B90 cm²
- C120 cm²
- D180 cm²
Area question 19 of 24+Show Answer & Explanation
Answer: B. 90 cm²
Explanation: ½ × 20 × 9 = 90 cm².
Q20.The circumference of a circle of radius 14 cm (π = 22/7) is:
Moderate- A44 cm
- B66 cm
- C88 cm
- D154 cm
Area question 20 of 24+Show Answer & Explanation
Answer: C. 88 cm
Explanation: 2πr = 2 × 22/7 × 14 = 88 cm.
Q21.If the side of a square is doubled, its area becomes:
Moderate- A2 times
- B3 times
- C4 times
- D8 times
Area question 21 of 24+Show Answer & Explanation
Answer: C. 4 times
Explanation: Area varies as the square of the side, so it becomes 2² = 4 times.
Q22.The area of a rhombus with diagonals 10 cm and 24 cm is:
Moderate- A60 cm²
- B120 cm²
- C240 cm²
- D480 cm²
Area question 22 of 24+Show Answer & Explanation
Answer: B. 120 cm²
Explanation: ½ × 10 × 24 = 120 cm².
Q23.A square and a rectangle have equal perimeters. If the square's side is 12 cm and the rectangle's length is 16 cm, the rectangle's breadth is:
Difficult- A6 cm
- B8 cm
- C10 cm
- D12 cm
Area question 23 of 24+Show Answer & Explanation
Answer: B. 8 cm
Explanation: Perimeter = 48 cm → 2(16 + b) = 48 → b = 8 cm.
Q24.The area of a circle is 154 cm² (π = 22/7). Its radius is:
Moderate- A5 cm
- B7 cm
- C11 cm
- D14 cm
Area question 24 of 24+Show Answer & Explanation
Answer: B. 7 cm
Explanation: πr² = 154 → r² = 154 × 7/22 = 49 → r = 7 cm.
Area — Frequently Asked Questions
Why does a 20% increase and a 20% decrease not cancel out for area?+
Because area multiplies the two dimensions: 1.20 × 0.80 = 0.96, a 4% decrease. Use the formula a + b + ab/100 with signs to get this in one step.
When should I use π = 22/7 instead of 3.14?+
Use 22/7 whenever the radius or diameter is a multiple of 7 — the sevens cancel and the arithmetic becomes exact. Otherwise 3.14 is usually more convenient.
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