CAT Geometry Questions PDF: Topic-Wise Practice Questions with Solutions

Geometry is one of the topics you should include in your CAT Quantitative Aptitude practice. These CAT Geometry Questions cover triangles, circles, quadrilaterals, polygons, area, angles and related concepts. The questions are arranged to give you practice with different types of problems that can appear in CAT.

If you are preparing for CAT 2026, solve these questions with a timer and check the solution only after making your own attempt. You can also download the CAT Geometry Questions PDF for offline practice and use the questions again during your revision.

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What are CAT Geometry Questions?

CAT Geometry Questions are those math problems in the Quant section that deal with shapes, lines, and figures.You’ll find topics like triangles, circles, polygons, and even coordinate geometry popping up here.

They aren’t just about formulas you need to visualize and apply concepts smartly.
With the right theorems and shortcuts, these CAT coordinate geometry questions can actually become some of the easiest to crack.

Download 100+ CAT Geometry Questions PDF for Practice

Importance of CAT Geometry Questions 2026

Geometry is one of the topics covered under the Quantitative Aptitude section of the CAT Syllabus. It includes concepts such as triangles, circles, quadrilaterals, angles, coordinate geometry and mensuration. The number of questions can vary from year to year, so it is better to focus on understanding the concepts rather than expecting a fixed number of Geometry questions in the exam.

Most CAT Geometry questions are based on basic properties, formulas and their application. Once you are comfortable with these concepts, you can solve many questions without spending too much time on lengthy calculations. This makes regular practice important, especially for topics like triangles, circles and coordinate geometry.

Before moving to advanced questions, make sure your basic properties and formulas are clear. You can also practise CAT Geometry Questions along with previous year questions to understand how these concepts are asked in the exam.

If you are revising Geometry before the exam, keep the important CAT Geometry Formulas handy. Revising them regularly and applying them to different questions can help you improve both speed and accuracy.

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Solve these CAT Geometry Questions 2026 to Boost Your CAT Scores

Easy Level CAT Geometry Questions to Practice

Q1. What is the area of a square with side length 6 cm?
A. 36 cm²
B. 12 cm²
C. 18 cm²
D. 24 cm²

Answer: A. 36 cm²

Q2. Find the perimeter of a rectangle with length 8 cm and width 3 cm.
A. 22 cm
B. 24 cm
C. 26 cm
D. 20 cm

Answer: A. 22 cm

Q3. What is the circumference of a circle with radius 7 cm? (Use π = 22/7)
A. 44 cm
B. 49 cm
C. 38.5 cm
D. 42 cm

Answer: A. 44 cm

Q4. A triangle has sides of lengths 3 cm, 4 cm, and 5 cm. What type of triangle is it?

A. Equilateral
B. Isosceles
C. Right-angled
D. Scalene

Answer: C. Right-angled

Q5. What is the area of a triangle with base 10 cm and height 5 cm?
A. 25 cm²
B. 50 cm²
C. 30 cm²
D. 20 cm²

Answer: A. 25 cm²

Q6. A circle has a diameter of 14 cm. What is its area? (Use π = 22/7)
A. 154 cm²
B. 77 cm²
C. 100 cm²
D. 121 cm²

Answer: A. 154 cm²

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Q7. Find the length of the diagonal of a square with side length 5 cm.
A. 5√2 cm
B. 10 cm
C. 7 cm
D. 6√2 cm

Answer: A. 5√2 cm

Q8. What is the sum of interior angles of a hexagon?
A. 540°
B. 720°
C. 900°
D. 1080°

Answer: B. 720°

Medium Level CAT Geometry Questions 

Q9. In a triangle, two sides are 7 cm and 10 cm, and the included angle is 60°. Find the area of the triangle.
A. 35√3 cm²
B. 35 cm²
C. 70 cm²
D. 30√3 cm²

Answer: A. 35√3 cm²

Q10. A parallelogram has base 12 cm and height 5 cm. Find its area.
A. 60 cm²
B. 30 cm²
C. 24 cm²
D. 70 cm²

Answer: A. 60 cm

Q11. The diagonals of a rhombus are 10 cm and 24 cm. Find its area.
A. 120 cm²
B. 100 cm²
C. 130 cm²
D. 140 cm²

Answer: A. 120 cm

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Q12. A circle is inscribed in a square. If the square has side length 14 cm, find the area of the circle. (Use π = 22/7)
A. 154 cm²
B. 308 cm²
C. 100 cm²
D. 121 cm²

Answer: A. 154 cm²

Q13. The sides of a triangle are in the ratio 3:4:5. If the perimeter is 36 cm, find the area.
A. 54 cm²
B. 72 cm²
C. 36 cm²
D. 60 cm²

Answer: A. 54 cm²

Q14. The height of an equilateral triangle is 6√3 cm. What is the area?
A. 54 cm²
B. 36√3 cm²
C. 72 cm²
D. 27√3 cm²

Answer: B. 36√3 cm²

Q15. The radius of a semicircle is 7 cm. Find its area.
A. 77 cm²
B. 154 cm²
C. 38.5 cm²
D. 100 cm²

Answer: A. 77 cm²

Q16. A triangle has sides 6 cm, 8 cm, and 10 cm. What is its area?
A. 24 cm²
B. 48 cm²
C. 30 cm²
D. 60 cm²

Answer: A. 24 cm²

Q17. What is the inradius of a triangle with area 84 cm² and semi-perimeter 14 cm?
A. 6 cm
B. 5 cm
C. 7 cm
D. 4 cm

Answer: A. 6 cm

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CAT Geometry Difficulty Level Questions

Q18. The length of each side of a regular hexagon is 6 cm. Find the area.
A. 93.53 cm²
B. 93.6 cm²
C. 93 cm²
D. 94.53 cm²

Answer: A. 93.53 cm²

Q19. The length of the diagonal of a square is 10√2 cm. Find its area.
A. 200 cm²
B. 100 cm²
C. 150 cm²
D. 250 cm²

Answer: B. 100 cm²

Q20. A triangle has sides 13 cm, 14 cm, and 15 cm. What is its area?
A. 84 cm²
B. 90 cm²
C. 70 cm²
D. 75 cm²

Answer: A. 84 cm²

Q21. The sides of a triangle are 10 cm, 24 cm, and 26 cm. What is the radius of the incircle?
A. 6 cm
B. 4 cm
C. 5 cm
D. 7 cm

Answer: B. 4 cm

Q22. In a circle of radius 14 cm, find the area of the sector with angle 45°.
A. 77 cm²
B. 38.5 cm²
C. 27.5 cm²
D. 30.25 cm²

Answer: A. 77 cm²

Q23. The difference between the circumradius and inradius of an equilateral triangle of side 6 cm is:
A. 2 cm
B. 3 cm
C. 1 cm
D. √3 cm

Answer: D. √3 cm

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Q24. A trapezium has parallel sides 10 cm and 6 cm and height 5 cm. Find its area.
A. 40 cm²
B. 50 cm²
C. 45 cm²
D. 55 cm²

Answer: A. 40 cm²

Q25. In a circle, two chords AB and CD are equidistant from the center. If AB = 12 cm, then CD is:
A. 12 cm
B. 10 cm
C. Cannot be determined
D. 14 cm

Answer: A. 12 cm

Q26. A cube has a surface area of 150 cm². What is the length of each side?

A. 5 cm
B. √25 cm
C. √150 cm
D. 10 cm

Answer: A. 5 cm

Q27. A rectangular field is 60 m long and 40 m wide. A path of 2 m is constructed inside along all sides. Find the area of the path.

A. 392 m²
B. 404 m²
C. 408 m²
D. 416 m²

Answer: A. 392 m²

Q28. The area of a rhombus is 120 cm². One diagonal is 12 cm. Find the other diagonal.

A. 20 cm
B. 15 cm
C. 10 cm
D. 18 cm

Answer: A. 20 cm

Q29. A cone has a base radius 7 cm and height 24 cm. What is its slant height?

A. 25 cm
B. 26 cm
C. 24.5 cm
D. 23 cm

Answer: A. 25 cm

Formulas for CAT Geometry Questions 2026

Here are some important formulas to use in geometry CAT level questions:

Basic Shapes In CAT Coordinate Geometry Questions

1. Triangle

• Area: A = 1/2 * base * height
• Perimeter: P = base + side + side (where base and side represent the lengths of the triangle's sides)

2. Rectangle

• Area: A = length * width
• Perimeter: P = 2(length + width)

3. Square

• Area: A = side² (where side represents the length of a square's side)
• Perimeter: P = 4(side)

4. Circle

• Area: A = πr² (where π is a constant value approximately equal to 3.14 and r represents the circle's radius)
• Circumference: C = 2πr

Lines and Angles In Geometry CAT Level Questions

• Straight Angle: measure is 180 degrees
• Right Angle: measure is 90 degrees
• Complementary Angles: two angles that add up to 90 degrees
• Supplementary Angles: two angles that add up to 180 degrees

Theorems For Geometry And Mensuration Questions For CAT

• Pythagorean Theorem: a² + b² = c² (where a and b represent the lengths of the legs of a right triangle, and c represents the length of the hypotenuse)

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Important Topics Covered in CAT Geometry

The CAT Geometry section mainly covers shapes, angles, measurements and coordinate-based concepts. Here's a quick look at the topics you should revise before solving questions:

Topic	What to Study
Triangles	Properties, similarity, congruence, Pythagoras, area, perimeter and Heron's Formula
Circles	Chords, tangents, radius, diameter, area, circumference and angles
Quadrilaterals	Square, rectangle, rhombus, parallelogram, trapezium, diagonals and area
Polygons	Interior/exterior angles, regular polygons, diagonals and perimeter
Lines & Angles	Parallel lines, transversals, angle relationships and basic theorems
Coordinate Geometry	Points, distance, midpoint, slope and equation of a line
Mensuration	Area, perimeter, surface area and volume of 2D and 3D figures

These topics cover the basic concepts you need before moving to more challenging CAT Geometry Questions. Start with individual topics and then solve mixed questions to see how different concepts are combined.

How to Solve CAT Geometry Questions

Geometry questions can look confusing at first, especially when the figure contains several lines, angles or shapes. The easiest way to handle them is to break the question into smaller parts instead of trying to solve everything at once. Practising CAT previous year papers can also help you understand how these concepts are framed in the exam and get familiar with different types of Geometry questions.

Follow these steps while practising CAT Geometry Questions:

1. Read the question carefully: First understand what is given and what you need to find. Don't start calculating before you know what the question is asking.
2. Mark the given values: Write down the lengths, angles, radius or other information provided in the question. Marking them on the figure can make the question easier to understand.
3. Identify the concept: Check whether the question is based on a triangle property, circle theorem, angle relationship, area formula or another Geometry concept.
4. Draw or extend the figure if needed: Some questions become much easier when you draw an additional line, divide a shape into smaller parts or extend one of the existing lines.
5. Apply the required formula or property: Once you know the concept, substitute the given values and solve step by step. Avoid using a formula if you are not sure what it represents.
6. Check your answer: Before moving on, quickly check whether the answer makes sense based on the figure and the values given.

With regular practice, you'll start recognising which property or formula is needed without spending too much time on the question.

Best Preparation Books for CAT Geometry Questions

Here is a list of some of the best books for CAT Geometry questions that are widely recommended by experts and toppers

Book Title	Author/Publisher	Key Features
How to Prepare for Quantitative Aptitude for the CAT	Arun Sharma	Comprehensive geometry coverage with level-wise CAT-oriented questions.
Quantitative Aptitude Quantum CAT	Sarvesh K. Verma	Includes advanced geometry problems, shortcuts, and detailed solutions.
Quantitative Aptitude for Competitive Examinations	R.S. Aggarwal	Ideal for building core geometry concepts with ample practice CAT geometry pyq.

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Conclusion

CAT Geometry Questions form an essential part of the CAT Exam and can greatly influence your Quantitative Aptitude score. With consistent preparation, a clear understanding of concepts, and regular practice, you can master geometry and perform well in the exam. Remember to focus on the key areas like lines, angles, triangles, circles, and coordinate geometry while also developing time-management skills. 

By following a structured approach, CAT Coordinate geometry questions can become one of your strongest sections in the CAT exam