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CSAT · 20 questions

Geometry & mensuration

Every UPSC CSAT question on this topic, 2016–2026, newest first. Tap an option to check yourself; the answer and explanation open below it.

Geometry & mensuration questions per year: 2016: 6, 2017: 1, 2018: 3, 2019: 0, 2020: 3, 2021: 2, 2022: 2, 2023: 2, 2024: 1, 2025: 0, 2026: 0 Asked in 8 of 11 years · most in 2016 (6)

UPSC syllabus: “Basic numeracy (numbers and their relations, orders of magnitude, etc.) (Class X level), Data interpretation (charts, graphs, tables, data sufficiency etc. — Class X level);” See the full syllabus →

CSAT 2022 · Q56

Easy

There are eight equidistant points on a circle. How many right-angled triangles can be drawn using these points as vertices and taking the diameter as one side of the triangle?

Answer & explanation

Answer: (a) 24

Eight equidistant points form 4 diameters. The angle in a semicircle is a right angle, so each diameter with any of the other 6 points gives a right-angled triangle: 4 × 6 = 24.

  1. With 8 equidistant points, each point has a point exactly opposite it, giving 8 ÷ 2 = 4 diameters.
  2. The angle in a semicircle is a right angle, so a diameter with any third point forms a right-angled triangle.
  3. Each diameter can pair with any of the other 6 points: 4 × 6 = 24 triangles.

Remember · Angle in a semicircle = 90°: count diameters × remaining points.

Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2022 · Q59

Medium

Consider the following statements in respect of a rectangular sheet of length 20 cm and breadth 8 cm:

  1. 1.It is possible to cut the sheet exactly into 4 square sheets.
  2. 2.It is possible to cut the sheet into 10 triangular sheets of equal area.

Which of the above statements is/are correct?

Answer & explanation

Answer: (c) Both 1 and 2

Two 8 cm squares plus two 4 cm squares use up the whole 20 × 8 sheet, and five 4 × 8 strips cut along their diagonals give 10 equal triangles. Both statements are possible.

  1. Statement 1: cut two 8 × 8 squares from the 20 × 8 sheet, leaving a 4 × 8 strip; cut that into two 4 × 4 squares. That is exactly 4 square sheets with nothing left over.
  2. Statement 2: cut the sheet into five 4 × 8 rectangles and cut each along a diagonal: 10 triangles, each of area 16 cm² (160 ÷ 10).
  3. Both statements are correct.
  • ✓ 1. 8 × 8 + 8 × 8 + 4 × 4 + 4 × 4 = 64 + 64 + 16 + 16 = 160 cm², the whole sheet.
  • ✓ 2. Five 4 × 8 rectangles halved diagonally give 10 triangles of 16 cm² each.

Remember · ‘It is possible’ needs only one construction; the squares need not be equal unless the item says so.

Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

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