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CAT QuantGeometryMensuration

CAT Quant Geometry and Mensuration: Formulas and Strategy

PrepTest Hub Team •Edited by BITS Pilani and IIM alumni •October 30, 2026

Key takeaways

  • Geometry and mensuration make up a regular part of Quant, and the formulas are short.
  • Learn triangles and circles first, then polygons and solids.
  • Always draw the diagram, label what you know, and look for similar triangles and right angles.
  • Practise recognising standard triples and shapes so you can skip long calculations.

Geometry questions in CAT Quant reward preparation more than raw talent: the formulas are finite, and the same ideas repeat. Pair this guide with the formula sheet and the geometry practice tests under CAT Quant. Use it to decide what to learn and in what order.

Learn in this order

  1. Triangles: angle sum, similarity, Pythagoras, area.
  2. Circles: chords, tangents, angles in a circle.
  3. Polygons and quadrilaterals.
  4. Coordinate geometry basics.
  5. Mensuration: areas and volumes of solids.

Triangle essentials

  • Area is half base times height, or half the product of two sides and the sine of the angle between them.
  • Heron's formula: area is the square root of s(s-a)(s-b)(s-c), where s is half the perimeter.
  • Right triangle: the inradius is (a + b - c) divided by 2, where c is the hypotenuse.
  • Circumradius is abc divided by four times the area.
  • Similar triangles have sides in the same ratio, and areas in the square of that ratio.

Circle essentials

  • The angle in a semicircle is a right angle.
  • The angle at the centre is twice the angle at the circumference on the same arc.
  • Tangents drawn from one point have equal length.
  • Intersecting chords: the products of the segments are equal.

Mensuration essentials

  • Cylinder: volume pi r squared h, curved surface 2 pi r h.
  • Cone: volume one third pi r squared h.
  • Sphere: volume four thirds pi r cubed, surface 4 pi r squared.
  • Cuboid: the space diagonal is the square root of (l squared + b squared + h squared).
  • Regular hexagon with side a: area is (3 root 3 over 2) a squared.

Strategy for the exam

  1. Draw a clean, large diagram and mark every given length and angle.
  2. Look for right angles, similar triangles and standard triples such as 3-4-5, 5-12-13 and 8-15-17.
  3. Use ratios and scaling before long arithmetic. If a length doubles, the area quadruples.
  4. Skip a question if the diagram is complex and you cannot see the first step in about 30 seconds.

How to practise

Do 8 to 10 geometry questions a day for two weeks, in timed sets. After each set, write the key idea of every question you missed. Our section time management guide explains how to decide when to skip.

Formulas are standard school mathematics. Check them against your own textbook, and use this guide as a study aid.

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