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XAT Geometry Questions with Answers & Explanations

20 Geometry questions from the Quantitative Ability & Data Interpretation section of XAT, 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.

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Question 1

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

  1. A36 cm²
  2. B72 cm²
  3. C45 cm²
  4. D42 cm²
  5. E30 cm²
Show answer
Answer: (A) 36 cm² Using Heron's formula, s = 18 and area = 36 cm².
Question 2

What is each interior angle of a regular polygon with 18 sides?

  1. A160°
  2. B170°
  3. C20°
  4. D154°
  5. ENone of these
Show answer
Answer: (A) 160° Interior angle = 180°(n − 2)/n = 160°.
Question 3

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

  1. A18 cm²
  2. B48 cm²
  3. C36 cm²
  4. D30 cm²
  5. E24 cm²
Show answer
Answer: (E) 24 cm² Using Heron's formula, s = 12 and area = 24 cm².
Question 4

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. B26 cm
  3. C25 cm
  4. D23 cm
  5. ENone of these
Show answer
Answer: (C) 25 cm Hypotenuse = √(7² + 24²) = 25 cm.
Question 5

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

  1. A16 : 25
  2. B5 : 6
  3. C4 : 5
  4. D64 : 125
  5. ENone of these
Show answer
Answer: (A) 16 : 25 The ratio of areas of similar triangles equals the square of the ratio of sides.
Question 6

What is each interior angle of a regular polygon with 12 sides?

  1. A144°
  2. B160°
  3. C150°
  4. D30°
  5. ENone of these
Show answer
Answer: (C) 150° Interior angle = 180°(n − 2)/n = 150°.
Question 7

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

  1. A42 cm²
  2. B36 cm²
  3. C45 cm²
  4. D30 cm²
  5. E72 cm²
Show answer
Answer: (B) 36 cm² Using Heron's formula, s = 18 and area = 36 cm².
Question 8

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

  1. A15 cm
  2. B21 cm
  3. C16 cm
  4. D13 cm
  5. ENone of these
Show answer
Answer: (A) 15 cm Hypotenuse = √(9² + 12²) = 15 cm.
Question 9

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

  1. A78 cm²
  2. B90 cm²
  3. C84 cm²
  4. D168 cm²
  5. E91 cm²
Show answer
Answer: (C) 84 cm² Using Heron's formula, s = 21 and area = 84 cm².
Question 10

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

  1. A10 cm
  2. B8 cm
  3. C9 cm
  4. D11 cm
  5. E14 cm
Show answer
Answer: (A) 10 cm Hypotenuse = √(6² + 8²) = 10 cm.

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Question 11

The corresponding sides of two similar triangles are in the ratio 1 : 2. What is the ratio of their areas?

  1. A1 : 2
  2. B1 : 4
  3. C2 : 3
  4. D1 : 8
  5. ENone of these
Show answer
Answer: (B) 1 : 4 The ratio of areas of similar triangles equals the square of the ratio of sides.
Question 12

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

  1. A156°
  2. B162°
  3. C18°
  4. D172°
  5. ENone of these
Show answer
Answer: (B) 162° Interior angle = 180°(n − 2)/n = 162°.
Question 13

What is the area of a triangle with sides 5 cm, 12 cm and 13 cm?

  1. A42 cm²
  2. B30 cm²
  3. C24 cm²
  4. D60 cm²
  5. E36 cm²
Show answer
Answer: (B) 30 cm² Using Heron's formula, s = 15 and area = 30 cm².
Question 14

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

  1. A8 : 125
  2. B3 : 6
  3. C4 : 25
  4. D2 : 5
  5. ENone of these
Show answer
Answer: (C) 4 : 25 The ratio of areas of similar triangles equals the square of the ratio of sides.
Question 15

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

  1. A408 cm²
  2. B204 cm²
  3. C210 cm²
  4. D198 cm²
  5. E212.5 cm²
Show answer
Answer: (B) 204 cm² Using Heron's formula, s = 34 and area = 204 cm².
Question 16

In a right-angled triangle, the two sides containing the right angle are 15 cm and 20 cm. What is the hypotenuse?

  1. A25 cm
  2. B35 cm
  3. C26 cm
  4. D23 cm
  5. E21 cm
Show answer
Answer: (A) 25 cm Hypotenuse = √(15² + 20²) = 25 cm.
Question 17

What is each interior angle of a regular polygon with 12 sides?

  1. A144°
  2. B160°
  3. C30°
  4. D150°
  5. ENone of these
Show answer
Answer: (D) 150° Interior angle = 180°(n − 2)/n = 150°.
Question 18

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

  1. A78 cm²
  2. B84 cm²
  3. C168 cm²
  4. D91 cm²
  5. E90 cm²
Show answer
Answer: (B) 84 cm² Using Heron's formula, s = 21 and area = 84 cm².
Question 19

In a right-angled triangle, the two sides containing the right angle are 5 cm and 12 cm. What is the hypotenuse?

  1. A17 cm
  2. B14 cm
  3. C13 cm
  4. D11 cm
  5. ENone of these
Show answer
Answer: (C) 13 cm Hypotenuse = √(5² + 12²) = 13 cm.
Question 20

What is each interior angle of a regular polygon with 8 sides?

  1. A145°
  2. B135°
  3. C45°
  4. D129°
  5. ENone of these
Show answer
Answer: (B) 135° Interior angle = 180°(n − 2)/n = 135°.

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

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