MCQs / Mathematics / Polygons, Triangles and Parallelograms

Polygons, Triangles and Parallelograms MCQs — Mathematics

28 multiple-choice questions on Polygons, Triangles and Parallelograms from Mathematics, each with the correct answer and, where available, a teacher's explanation. Read through them to revise the chapter, then practise the same questions one by one to test yourself.

1. Each interior angle of a regular polygon is 140^circ. The number of sides is:

  1. 7
  2. 9
  3. 14
  4. 12

Answer: B) 9

Explanation: Exterior angle = 180^circ - 140^circ = 40^circ, so n = 36040 = 9. SLO M-09-B-18 · Application

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2. Why can't regular pentagons tile a floor by themselves?

  1. their sides are unequal
  2. they have 5 sides
  3. their angles add up to 540^circ
  4. 108^circ does not divide 360^circ exactly

Answer: D) 108^circ does not divide 360^circ exactly

Explanation: 360 div 108 = 3.33ldots, so they leave gaps. SLO M-09-B-18 · Application

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3. Each interior angle of a regular pentagon is:

  1. 118^circ
  2. 540^circ
  3. 108^circ
  4. 72^circ

Answer: C) 108^circ

Explanation: Each interior angle = (n - 2) 180^circn = 3 180^circ5 = 108^circ. SLO M-09-B-18 · Application

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4. Each exterior angle of a regular polygon is 72^circ. How many sides does it have?

  1. 2
  2. 36
  3. 7
  4. 5

Answer: D) 5

Explanation: n = 360^circ72^circ = 5. SLO M-09-B-18 · Application

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5. Each exterior angle of a regular 20-sided polygon is:

  1. 162^circ
  2. 18^circ
  3. 9^circ
  4. 200^circ

Answer: B) 18^circ

Explanation: Exterior angles add up to 360^circ: 360^circ20 = 18^circ. SLO M-09-B-18 · Application

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6. Each interior angle of a regular octagon is:

  1. 135^circ
  2. 45^circ
  3. 1080^circ
  4. 145^circ

Answer: A) 135^circ

Explanation: Each interior angle = (n - 2) 180^circn = 6 180^circ8 = 135^circ. SLO M-09-B-18 · Application

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7. The sum of the interior angles of a polygon with 7 sides is:

  1. 900^circ
  2. 360^circ
  3. 1260^circ
  4. 1080^circ

Answer: A) 900^circ

Explanation: (n - 2) 180^circ = 5 180^circ = 900^circ. SLO M-09-B-18 · Application

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8. A wall 6 m long and 3 m high has a window 1.5 m by 1.2 m. Paint costs Rs. 120 per m². The cost to paint the wall is:

  1. Rs. 216
  2. Rs. 2,160
  3. Rs. 1,800
  4. Rs. 1,944

Answer: D) Rs. 1,944

Explanation: Area = 18 - 1.8 = 16.2 m²; 16.2 120 = 1944. SLO M-09-B-18 · Application

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9. A parallelogram-shaped plot has base 12 m and height 8 m. Turfing costs Rs. 450 per m². The total cost is:

  1. Rs. 18,000
  2. Rs. 21,600
  3. Rs. 43,200
  4. Rs. 9,000

Answer: C) Rs. 43,200

Explanation: Area = 12 8 = 96 m²; cost = 96 450 = 43200. SLO M-09-B-18 · Application

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10. A triangular sail has base 20 m and height 11 m. Its area is:

  1. 220 m²
  2. 55 m²
  3. 31 m²
  4. 110 m²

Answer: D) 110 m²

Explanation: 12 20 11 = 110 m². SLO M-09-B-18 · Application

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11. Each interior angle of a regular decagon is:

  1. 154^circ
  2. 36^circ
  3. 144^circ
  4. 1440^circ

Answer: C) 144^circ

Explanation: Each interior angle = (n - 2) 180^circn = 8 180^circ10 = 144^circ. SLO M-09-B-18 · Application

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12. A regular hexagonal garden has side 7 m. Fencing costs Rs. 350 per metre. The fencing costs:

  1. Rs. 2,450
  2. Rs. 12,250
  3. Rs. 17,150
  4. Rs. 14,700

Answer: D) Rs. 14,700

Explanation: Perimeter = 6 7 = 42 m; 42 350 = 14,700. SLO M-09-B-18 · Application

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13. An architect designs a regular octagonal gazebo. The angle between two neighbouring sides (inside) is:

  1. 150^circ
  2. 120^circ
  3. 45^circ
  4. 135^circ

Answer: D) 135^circ

Explanation: 6 180^circ8 = 135^circ. SLO M-09-B-18 · Application

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14. The sum of the interior angles of a polygon with 14 sides is:

  1. 2160^circ
  2. 2340^circ
  3. 360^circ
  4. 2520^circ

Answer: A) 2160^circ

Explanation: (n - 2) 180^circ = 12 180^circ = 2160^circ. SLO M-09-B-18 · Application

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15. Each exterior angle of a regular polygon is 30^circ. How many sides does it have?

  1. 12
  2. 6
  3. 15
  4. 14

Answer: A) 12

Explanation: n = 360^circ30^circ = 12. SLO M-09-B-18 · Application

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16. The sum of the interior angles of a polygon with 11 sides is:

  1. 1980^circ
  2. 360^circ
  3. 1800^circ
  4. 1620^circ

Answer: D) 1620^circ

Explanation: (n - 2) 180^circ = 9 180^circ = 1620^circ. SLO M-09-B-18 · Application

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17. Each interior angle of a regular polygon is 156^circ. The number of sides is:

  1. 18
  2. 16
  3. 13
  4. 15

Answer: D) 15

Explanation: Exterior angle = 180^circ - 156^circ = 24^circ, so n = 36024 = 15. SLO M-09-B-18 · Application

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18. Each exterior angle of a regular polygon is 40^circ. How many sides does it have?

  1. 20
  2. 4
  3. 9
  4. 11

Answer: C) 9

Explanation: n = 360^circ40^circ = 9. SLO M-09-B-18 · Application

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19. Each exterior angle of a regular polygon is 24^circ. How many sides does it have?

  1. 7
  2. 17
  3. 12
  4. 15

Answer: D) 15

Explanation: n = 360^circ24^circ = 15. SLO M-09-B-18 · Application

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20. Which regular polygons can tile a floor on their own without gaps?

  1. regular pentagons and octagons
  2. equilateral triangles, squares and regular hexagons
  3. any regular polygon
  4. only squares

Answer: B) equilateral triangles, squares and regular hexagons

Explanation: Their interior angles (60^circ, 90^circ, 120^circ) divide 360^circ exactly. SLO M-09-B-18 · Application

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21. How many square tiles of side 25 cm are needed to cover a floor 5 m by 3 m?

  1. 60
  2. 120
  3. 240
  4. 375

Answer: C) 240

Explanation: Floor = 500 300 = 150,000 cm²; tile = 625 cm²; 150,000 div 625 = 240. SLO M-09-B-18 · Application

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22. A room is 5 m by 4 m. Carpet costs Rs. 950 per m². Carpeting the floor costs:

  1. Rs. 9,500
  2. Rs. 8,550
  3. Rs. 19,000
  4. Rs. 17,100

Answer: C) Rs. 19,000

Explanation: 5 4 = 20 m²; 20 950 = 19,000. SLO M-09-B-18 · Application

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23. Each interior angle of a regular dodecagon is:

  1. 150^circ
  2. 160^circ
  3. 30^circ
  4. 1800^circ

Answer: A) 150^circ

Explanation: Each interior angle = (n - 2) 180^circn = 10 180^circ12 = 150^circ. SLO M-09-B-18 · Application

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24. Each interior angle of a regular hexagon is:

  1. 130^circ
  2. 120^circ
  3. 720^circ
  4. 60^circ

Answer: B) 120^circ

Explanation: Each interior angle = (n - 2) 180^circn = 4 180^circ6 = 120^circ. SLO M-09-B-18 · Application

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25. Each exterior angle of a regular 15-sided polygon is:

  1. 12^circ
  2. 24^circ
  3. 156^circ
  4. 150^circ

Answer: B) 24^circ

Explanation: Exterior angles add up to 360^circ: 360^circ15 = 24^circ. SLO M-09-B-18 · Application

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