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NDA & NA Geometry Questions with Answers & Explanations

20 Geometry questions from the Mathematics section of NDA & NA, each with the correct answer and a worked explanation. Try each question first, then tap Show answer to check. When you're ready, take the timed chapter-wise test to see your all-India rank.

NDA & NA full mocks
Question 1

What is each interior angle of a regular polygon with 10 sides?

  1. A144°
  2. B154°
  3. C138°
  4. D36°
Show answer
Answer: (A) 144° Interior angle = 180°(n − 2)/n = 144°.
Question 2

In a right-angled triangle, the two sides containing the right angle are 12 cm and 16 cm. What is the hypotenuse?

  1. A28 cm
  2. B20 cm
  3. C18 cm
  4. D21 cm
Show answer
Answer: (B) 20 cm Hypotenuse = √(12² + 16²) = 20 cm.
Question 3

The corresponding sides of two similar triangles are in the ratio 2 : 5. What is the ratio of their areas?

  1. A2 : 5
  2. B3 : 6
  3. C4 : 25
  4. D8 : 125
Show answer
Answer: (C) 4 : 25 The ratio of areas of similar triangles equals the square of the ratio of sides.
Question 4

What is the area of a triangle with sides 13 cm, 14 cm and 15 cm?

  1. A168 cm²
  2. B91 cm²
  3. C78 cm²
  4. D84 cm²
Show answer
Answer: (D) 84 cm² Using Heron's formula, s = 21 and area = 84 cm².
Question 5

What is each interior angle of a regular polygon with 5 sides?

  1. A102°
  2. B118°
  3. C108°
  4. D72°
Show answer
Answer: (C) 108° Interior angle = 180°(n − 2)/n = 108°.
Question 6

In a right-angled triangle, the two sides containing the right angle are 7 cm and 24 cm. What is the hypotenuse?

  1. A31 cm
  2. B25 cm
  3. C26 cm
  4. D23 cm
Show answer
Answer: (B) 25 cm Hypotenuse = √(7² + 24²) = 25 cm.
Question 7

The corresponding sides of two similar triangles are in the ratio 3 : 5. What is the ratio of their areas?

  1. A3 : 5
  2. B9 : 25
  3. C4 : 6
  4. D27 : 125
Show answer
Answer: (B) 9 : 25 The ratio of areas of similar triangles equals the square of the ratio of sides.
Question 8

What is the area of a triangle with sides 9 cm, 10 cm and 17 cm?

  1. A36 cm²
  2. B30 cm²
  3. C72 cm²
  4. D42 cm²
Show answer
Answer: (A) 36 cm² Using Heron's formula, s = 18 and area = 36 cm².
Question 9

In a right-angled triangle, the two sides containing the right angle are 9 cm and 12 cm. What is the hypotenuse?

  1. A21 cm
  2. B16 cm
  3. C15 cm
  4. D13 cm
Show answer
Answer: (C) 15 cm Hypotenuse = √(9² + 12²) = 15 cm.
Question 10

The corresponding sides of two similar triangles are in the ratio 4 : 5. What is the ratio of their areas?

  1. A4 : 5
  2. B64 : 125
  3. C16 : 25
  4. D5 : 6
Show answer
Answer: (C) 16 : 25 The ratio of areas of similar triangles equals the square of the ratio of sides.
Question 11

What is the area of a triangle with sides 17 cm, 25 cm and 26 cm?

  1. A204 cm²
  2. B408 cm²
  3. C212.5 cm²
  4. D210 cm²
Show answer
Answer: (A) 204 cm² Using Heron's formula, s = 34 and area = 204 cm².
Question 12

In a right-angled triangle, the two sides containing the right angle are 6 cm and 8 cm. What is the hypotenuse?

  1. A9 cm
  2. B11 cm
  3. C10 cm
  4. D14 cm
Show answer
Answer: (C) 10 cm Hypotenuse = √(6² + 8²) = 10 cm.
Question 13

What is each interior angle of a regular polygon with 6 sides?

  1. A120°
  2. B130°
  3. C60°
  4. D114°
Show answer
Answer: (A) 120° Interior angle = 180°(n − 2)/n = 120°.
Question 14

What is the area of a triangle with sides 10 cm, 10 cm and 12 cm?

  1. A54 cm²
  2. B50 cm²
  3. C96 cm²
  4. D48 cm²
Show answer
Answer: (D) 48 cm² Using Heron's formula, s = 16 and area = 48 cm².
Question 15

What is each interior angle of a regular polygon with 15 sides?

  1. A24°
  2. B150°
  3. C166°
  4. D156°
Show answer
Answer: (D) 156° Interior angle = 180°(n − 2)/n = 156°.
Question 16

What is the area of a triangle with sides 6 cm, 8 cm and 10 cm?

  1. A30 cm²
  2. B24 cm²
  3. C18 cm²
  4. D48 cm²
Show answer
Answer: (B) 24 cm² Using Heron's formula, s = 12 and area = 24 cm².
Question 17

The corresponding sides of two similar triangles are in the ratio 2 : 3. What is the ratio of their areas?

  1. A2 : 3
  2. B8 : 27
  3. C4 : 9
  4. D3 : 4
Show answer
Answer: (C) 4 : 9 The ratio of areas of similar triangles equals the square of the ratio of sides.
Question 18

What is each interior angle of a regular polygon with 15 sides?

  1. A150°
  2. B156°
  3. C166°
  4. D24°
Show answer
Answer: (B) 156° Interior angle = 180°(n − 2)/n = 156°.
Question 19

What is each interior angle of a regular polygon with 10 sides?

  1. A138°
  2. B154°
  3. C36°
  4. D144°
Show answer
Answer: (D) 144° Interior angle = 180°(n − 2)/n = 144°.
Question 20

What is each interior angle of a regular polygon with 20 sides?

  1. A18°
  2. B156°
  3. C162°
  4. D172°
Show answer
Answer: (C) 162° Interior angle = 180°(n − 2)/n = 162°.

These are RankerClub practice questions written in the NDA & NA pattern. They are not official SSC/IBPS/RRB papers.

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