CAT Geometry Questions with Solutions PDF; Preparation Guide, Types of Questions

Updated on Oct 21, 2026 01:38 IST

By Abhishek Dhawan, Deputy Manager - MBA & BBA Content

Geometry questions account for nearly 5 per cent of the entire CAT question paper. A good hold on Geometry can help candidates obtain a good score in the Quantitative Aptitude section and improve the sectional score. In each session of the CAT exam, candidates can expect 3-4 direct Geometry questions (this is roughly 15-20% of all Quantitative Aptitude questions). The test-taker must aim to solve each question in less than 2 minutes. Geometry questions are both MCQs and TITA type.

In the CAT exam, candidates find CAT Geometry questions on Triangles, Circles, and Quadrilaterals & Polygons. A good hold on Geometry also helps in advanced topics like 3D Mensuration, Coordinate Geometry, and Geometry-based Puzzles.

This article hosts some CAT Geometry questions. These questions are at par with the difficulty trends and CAT exam pattern, including MCQ and TITA questions. Candidates can practice CAT Geometry questions with solutions and with varied difficulty levels for holistic preparation for the CAT 2026 exam.

Table of contents

Sample CAT Geometry Questions with Solutions
CAT Geometry Syllabus & Important Topics
Important Geometry Formulas for CAT
Explore Topic Wise CAT Preparation Resources
FAQs on CAT Geometry Preparation

Sample CAT Geometry Questions with Solutions

Find a few questions from CAT Geometry with different difficulty levels:

Question 1: Let ABCD be a parallelogram such that the three coordinates of its three vertices A, B, C are (1, 1), (3, 4) and (-2, 8), respectively. Then the coordinates of the vertex D are:

(0, 11)
(4, 5)
(-3, 4)
(-4, 5)

Question 2: All the vertices of a rectangle lie on a circle of Radius R. If the perimeter of the Rectangle is P, then the area of rectangle is:

P²/16 – R²
P²/8 – 2R²
P²/2 – 2PR
P²/8 – R²/2

Question 3: Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle away form A, with diameter BC. Let BPCB be an arc of a circle centered at A and lying between BC and BQC. If AB has length 6 cm then the area, in sq cm, of the region enclosed by BPC and BQC is:

9 π- 18
18
9 π
9

Question 4: ABCD is a trapezium in which AB is parallel to CD. The sides AD and BC E when extended, intersect at point E. If AB= 2 cm, CD= 1 cm, and perimeter of ABCD is 6 cm, then the perimeter in cm, of Triangle AEB is:

Question 5: A Trapezium ABCD has side AD parallel to BC. ∠BAD = 90 °, BC = 3 cm and AD = 8 cm. If the perimeter of this trapezium in 36 cm, then its area in sq. cm, is?

Practice CAT Geometry Questions: Master core concepts in Triangles, Circles, and Mensuration.

CAT Geometry Practice Test

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CAT Geometry Syllabus & Important Topics

Conducting IIM does not release a dedicated syllabus PDF for CAT exam. CAT syllabus is curated after analysing the past question trends. Candidates preparing for Geometry in CAT exam should understand the basic properties of shapes, angles, triangles, circles and polygons. They should also practise questions based on area, perimeter and volume.

CAT exam does not have a fixed topic-wise question distribution. Therefore, candidates should prepare all major Geometry topics instead of focusing on only one area. Check the table below for Geometry syllabus for CAT exam:

Topic	Important Concepts
Lines and Angles	Parallel lines, transversals, complementary angles, supplementary angles and vertically opposite angles.
Triangles	Angle sum property, types of triangles, Pythagoras theorem, similarity, congruence, special triangles and area.
Circles	Radius, diameter, chords, tangents, arcs, angles in a circle and cyclic quadrilaterals.
Quadrilaterals	Properties of squares, rectangles, parallelograms, rhombuses and trapeziums.
Polygons	Interior angles, exterior angles, diagonals and properties of regular polygons.
Mensuration	Area, perimeter, surface area and volume of common two-dimensional and three-dimensional shapes.
Coordinate Geometry	Distance between two points, midpoint, slope of a line and basic equations of lines.

Turn Geometry into your Strongest CAT Topic: Master Triangles, Circles & Polygons, Coordinate Geometry, and key visualisation shortcuts.

CAT Geometry Guide

Important Geometry Formulas for CAT

The following tables cover important formulas for angles, triangles, quadrilaterals, circles, polygons and mensuration.

1. Lines and Angles

Property	Formula or Rule
Angles on a straight line	Angle 1 + Angle 2 = 180°
Angles around a point	Sum of angles = 360°
Complementary angles	Angle 1 + Angle 2 = 90°
Vertically opposite angles	Vertically opposite angles are equal.
Angles of a triangle	A + B + C = 180°

2. Triangle Formulas

Property	Formula
Perimeter	a + b + c
Area	½ × Base × Height
Heron's Formula	√[s(s − a)(s − b)(s − c)]
Semi-perimeter	s = (a + b + c) / 2
Pythagoras Theorem	Hypotenuse² = Base² + Perpendicular²
Equilateral triangle: Area	(√3 / 4) × a²
Equilateral triangle: Height	(√3 / 2) × a
Equilateral triangle: Perimeter	3a
Right-angled triangle: Area	½ × Base × Perpendicular

Note: In these formulas, a, b and c represent the sides of a triangle. The semi-perimeter is represented by s.

3. Quadrilateral Formulas

Shape	Area	Perimeter
Square	a²	4a
Rectangle	Length × Breadth	2 × (Length + Breadth)
Parallelogram	Base × Height	2 × (a + b)
Rhombus	½ × d₁ × d₂	4a
Trapezium	½ × (Sum of parallel sides) × Height	Sum of all four sides

Note: In the formulas, a represents the side of a square or rhombus, d₁ and d₂ represent the diagonals, and a and b in the parallelogram perimeter formula represent its two adjacent sides.

4. Circle Formulas

Property	Formula
Diameter	d = 2r
Circumference	2πr or πd
Area	πr²
Length of an arc	(θ / 360°) × 2πr
Area of a sector	(θ / 360°) × πr²

Note: Here, r is the radius, d is the diameter and θ is the central angle measured in degrees. The value of π is approximately 3.14 or 22/7.

5. Polygon Formulas

Property	Formula
Sum of interior angles	(n − 2) × 180°
Each interior angle of a regular polygon	[(n − 2) × 180°] / n
Each exterior angle of a regular polygon	360° / n
Number of diagonals	n(n − 3) / 2

Note: In these formulas, n represents the number of sides of the polygon.

6. Three-Dimensional Shapes: Mensuration Formulas

Shape	Volume	Surface Area
Cube	a³	Total surface area = 6a²
Cuboid	Length × Breadth × Height	2(lb + bh + hl)
Cylinder	πr²h	Total surface area = 2πr(r + h)
Cone	⅓πr²h	Total surface area = πr(r + l)
Sphere	(4/3)πr³	4πr²
Hemisphere	(2/3)πr³	Total surface area = 3πr²

Note: In these formulas, a is the side of a cube, l is the length of a cuboid or the slant height of a cone depending on the formula, b is the breadth, h is the vertical height and r is the radius. For the cuboid surface area formula, l represents length.

7. Coordinate Geometry Formulas

Property	Formula
Distance between two points	√[(x₂ − x₁)² + (y₂ − y₁)²]
Midpoint	((x₁ + x₂) / 2, (y₁ + y₂) / 2)
Slope of a line	(y₂ − y₁) / (x₂ − x₁), when x₂ ≠ x₁

Candidates should revise important formulas for CAT exam and practise applying them to questions.

Explore Topic Wise CAT Preparation Resources

Check the space below for CAT practice questions for topics other than Geometry:

CAT Topic-Wise Practice Questions

Practice by topic with questions and detailed solutions

📘 VARC Practice 7 Topics ▾

VARC → Para Summary → Verbal Ability → Para Jumbles → Odd One Out → Critical Reasoning → Vocabulary → Idioms →

📊 DILR Practice 5 Topics ▾

DILR→ DI→ LR→ Puzzles→ Seating Arrangement→

📐 Quant Practice 13 Topics ▾

Quant→ Arithmetic→ Algebra→ Number System→ Percentages→ Profit & Loss→ Averages→ Time & Work→ Probability→ Logarithms→ Trigonometry→ Time, Speed & Distance→

Explore More CAT Preparation Resources →

Candidates preparing for the exam can also use CAT previous year question papers.

FAQs on CAT Geometry Preparation

Find some frequently asked questions related to CAT Geometry questions and preparation:

Q: How many Geometry questions can I expect in the CAT exam?

Geometry is a an important topic in the Quantitative Aptitude (QA) section. Candidates can typically expect 3 to 5 questions out of the 22 total QA questions, making up roughly 15% to 20% of the section.

Q: Which sub-topics within Geometry are the most important for CAT exam?

Triangles (properties, similarity, congruence, and theorems) is the most heavily tested sub-topic in CAT exam. Other high-yield areas include Circles (tangents, chords, and cyclic quadrilaterals), Mensuration (area and volume of 2D/3D shapes), and Coordinate Geometry.

Q: Can I skip Geometry and still get a 99+ percentile in CAT Quants?

It is technically possible to get 99 percentile in CAT Quants if a candidates obtains a perfect score in Arithmetic and Algebra. However, it can be highly risky as CAT exam often has Geometry questions aligned with Algebra or Coordinate systems. Sometimes candidates must know two different concepts to solve one question. Therefore, skipping the entire module means leaving some questions from other topics as well.

Q: What is the best way to memorise all the Geometry formulas during CAT preparation?

Candidates must maintain a dedicated formula sheet for properties of polygons, circle theorems, and mensuration formulas. Instead of memorising blindly, candidates must solve 15-20 problems for each sub-topic to understand how and when to apply each formula.