Quantitative Aptitude

Mensuration: 2D: Practice Questions with Answers

16 practice questions on Mensuration: 2D, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.

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1. Q.1

   The diagonals of a rhombus are 16 cm and 12 cm. Find its area.

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   Answer: 96 cm²

   Solution:

   1. Area = (1/2) × d₁ × d₂
   2. = (1/2) × 16 × 12
   3. = 96 cm²

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2. Q.2

   A trapezium has parallel sides of length 10 cm and 14 cm, and the perpendicular distance between them is 6 cm. Find its area.

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   Answer: 72 cm²

   Solution:

   1. Area = (1/2) × (sum of parallel sides) × height
   2. = (1/2) × (10 + 14) × 6
   3. = (1/2) × 24 × 6 = 72 cm²

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3. Q.3

   Find the area of a right-angled triangle with base 12 cm and height 9 cm. Also find the length of its hypotenuse.

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   Answer: Area = 54 cm², Hypotenuse = 15 cm

   Solution:

   1. Area = (1/2) × base × height = (1/2) × 12 × 9 = 54 cm²
   2. Hypotenuse = √(base² + height²) = √(12² + 9²) = √(144 + 81) = √225 = 15 cm

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4. Q.4

   Find the area and perimeter of a rectangle with length 15 m and breadth 8 m.

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   Answer: Area = 120 m², Perimeter = 46 m

   Solution:

   1. Area = length × breadth = 15 × 8 = 120 m²
   2. Perimeter = 2(length + breadth) = 2(15 + 8) = 2 × 23 = 46 m

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5. Q.5

   Find the area of a parallelogram with base 12 cm and the perpendicular height between its parallel sides equal to 7 cm.

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   Answer: 84 cm²

   Solution:

   1. Area = base × height
   2. = 12 × 7
   3. = 84 cm²

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6. Q.6

   A rectangular garden is 20 m long and 15 m wide. A path 2.5 m wide is built all around it, on the outside. Find the area of the path.

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   Answer: 200 m²

   Solution:

   1. The path adds 2.5 m on every side, so the outer rectangle is (20 + 2×2.5) by (15 + 2×2.5) = 25 m by 20 m.
   2. Outer area = 25 × 20 = 500 m². Garden (inner) area = 20 × 15 = 300 m².
   3. Area of the path = outer area − inner area = 500 − 300 = 200 m²

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7. Q.7

   A triangle has sides 13 cm, 14 cm and 15 cm. Find its area using Heron's formula.

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   Answer: 84 cm²

   Solution:

   1. Semi-perimeter s = (13 + 14 + 15) / 2 = 21.
   2. Area = √(s(s−a)(s−b)(s−c)) = √(21 × (21−13) × (21−14) × (21−15))
   3. = √(21 × 8 × 7 × 6) = √7,056
   4. = 84 cm²

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8. Q.8

   A circular park has a radius of 14 m. Find its area. (Use π = 22/7.)

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   Answer: 616 m²

   Solution:

   1. Area = πr² = (22/7) × 14 × 14
   2. 14 is a multiple of 7, so it cancels cleanly: (22/7) × 14 = 44, then 44 × 14 = 616

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9. Q.9

   A rhombus has diagonals of 10 cm and 24 cm. Find its area.

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   Answer: 120 cm². Area = (1/2) × 10 × 24.

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10. Q.10

    A circular garden has a radius of 21 m. Find its area. (Use π = 22/7.)

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    Answer: 1,386 m²

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11. Q.11

    Find the area of a parallelogram with base 15 cm and height 8 cm.

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    Answer: 120 cm². Area = base × height.

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12. Q.12

    Find the area and arc length of a sector of radius 21 cm with a central angle of 60°. (Use π = 22/7.)

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    Answer: Area = 231 cm², Arc length = 22 cm. Area = (60/360) × (22/7) × 21²; arc = (60/360) × 2 × (22/7) × 21.

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13. Q.13

    A trapezium has parallel sides 8 cm and 12 cm with a height of 5 cm. Find its area.

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    Answer: 50 cm². Area = (1/2) × (8+12) × 5.

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14. Q.14

    Find the area of a right-angled triangle with base 10 cm and height 24 cm. Also find its hypotenuse.

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    Answer: Area = 120 cm², Hypotenuse = 26 cm

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15. Q.15

    Find the area and perimeter of a rectangle with length 18 m and breadth 10 m.

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    Answer: Area = 180 m², Perimeter = 56 m

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16. Q.16

    Find the area of an equilateral triangle with side 8 cm.

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    Answer: 16√3 cm² ≈ 27.7 cm². Area = (√3/4) × 8².

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