Extra Questions for Class 8 Maths Chapter 14: Area – HOTS

Fresh HOTS-level extra questions for Class 8 Maths Chapter 14 (Area), with numbers not found in the NCERT book. Full worked solutions included. These Class 8 Mathematics Chapter 14 important questions are handy for last-minute exam practice.

Q1 (Path around a garden, reverse problem). A rectangular garden has a uniform path of width 3 m around it. If the outer boundary measures 26 m × 20 m, find the area of the path.
Solution: Inner garden = (26−2×3) × (20−2×3) = 20 × 14 = 280 m². Outer area = 26×20 = 520 m². Area of path = 520 − 280 = 240 m².

Q2 (Triangle area from three points, using base-height). A triangle has a base of 9 cm and its area is 54 cm². Find its height.
Solution: Area = ½ × base × height ⇒ 54 = ½(9)(h) ⇒ h = 108/9 = 12 cm.

Q3 (Assertion–Reason). Assertion (A): Doubling only the base of a parallelogram (keeping height fixed) doubles its area. Reason (R): Area of a parallelogram = base × height.
Solution: R is true and correctly explains A: since Area = base × height, doubling the base while height stays fixed exactly doubles the product, hence doubles the area. Both A and R are true, and R correctly explains A.

Q4 (Trapezium, missing height). A trapezium has parallel sides 15 cm and 9 cm, and its area is 96 cm². Find its height.
Solution: 96 = ½(15+9)(h) = 12h ⇒ h = 8 cm.

Q5 (Rhombus, missing diagonal). A rhombus has area 210 cm² and one diagonal 21 cm. Find the other diagonal.
Solution: 210 = ½(21)(d₂) ⇒ d₂ = 420/21 = 20 cm.

Q6 (Composite figure). A plot is an L-shape formed by a 12 m × 8 m rectangle with a 4 m × 3 m rectangular notch cut from one corner. Find the remaining area.
Solution: Full rectangle = 12×8 = 96 m². Notch removed = 4×3 = 12 m². Remaining area = 96−12 = 84 m².

Q7 (Scaling reasoning). If a triangle’s base and height are both tripled, by what factor does its area increase?
Solution: Area = ½ × base × height. Tripling both: ½ × (3b) × (3h) = 9 × (½bh). The area increases by a factor of 9 (since both dimensions scale by 3, area scales by 3²=9).

Q8 (Unit conversion, HOTS). A rectangular plot measures 15 ft by 20 ft. Find its area in both ft² and m² (use 1 ft = 0.3048 m).
Solution: Area = 15×20 = 300 ft². In metres: 15 ft = 4.572 m, 20 ft = 6.096 m ⇒ Area = 4.572 × 6.096 ≈ 27.87 m².

Q9 (Spot the error). A student says: “Since a rhombus and a rectangle can have the same diagonals, they must have the same area.” Is this correct?
Solution: Incorrect. A rhombus’s area depends on ½ × d₁ × d₂ only because its diagonals are perpendicular bisectors of each other — that specific formula doesn’t apply to a general rectangle (whose area is length × width, not related to its diagonals the same way). Two shapes sharing the same diagonal lengths do not, in general, have the same area unless the diagonals play the same geometric role in both.

Q10 (Multi-step composite area). A trapezium-shaped field has parallel sides 40 m and 24 m with height 18 m. A circular pond of radius 7 m (use π=22/7) sits inside it. Find the usable (non-pond) area of the field.
Solution: Trapezium area = ½(40+24)(18) = ½(64)(18) = 576 m². Pond area = πr² = (22/7)(7²) = 22×7 = 154 m². Usable area = 576 − 154 = 422 m².

More on This Chapter

See also: NCERT Solutions for Class 8 Maths Chapter 14, Class 8 Maths NCERT Book and the Class 8 Maths Formulas Handbook.

Revision Notes: Revision Notes for Class 8 Maths Chapter 14

Written by Satish

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