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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)
Timed · 30 minutes a set Practise Geometry & mensuration as timed tests 1 set of about 20 questions with UPSC's CSAT marking. Start practising

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);” Sub-topics in the detailed syllabus →

CSAT 2022 · Q56

Easy

किसी वृत्त पर एक-समान दूरी वाले आठ बिन्दु हैं। इन बिन्दुओं को शीर्ष और व्यास को एक भुजा लेकर कितने समकोण त्रिभुज खींचे जा सकते हैं?

Read this question in English

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?

(a) 24 · (b) 16 · (c) 12 · (d) 8

उत्तर और व्याख्या · explanation in English

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

20 cm लम्बी और 8 cm चौड़ी आयताकार चादर के बारे में निम्नलिखित कथनों पर विचार कीजिए :

  1. 1.इस चादर को ठीक-ठीक 4 वर्गाकार चादरों में काटना सम्भव है।
  2. 2.इस चादर को समान क्षेत्रफल वाले 10 त्रिभुजाकार चादरों में काटना सम्भव है।

उपर्युक्त कथनों में से कौन-सा/से सही है/हैं?

Read this question in English

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

1. It is possible to cut the sheet exactly into 4 square sheets.

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

Which of the above statements is/are correct?

(a) 1 only · (b) 2 only · (c) Both 1 and 2 · (d) Neither 1 nor 2

उत्तर और व्याख्या · explanation in English

Answer: (c) 1 और 2 दोनों

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 ·

The Syllabus X-Ray of this topic

None of its 2 sub-topics is Core

0 Core · 0 High · 2 Steady · 0 Rare

The X-Ray ranks all 928 sub-topics of the UPSC syllabus by what UPSC has asked since 2016. The 6 CSAT Core sub-topics are behind 50% of CSAT questions.

See the whole X-Ray →

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