CAT Mensuration Bible Top 10 Must Solve Mensuration Questions covering 90% of Syllabus
Every real CAT question on this chapter from the past papers we have, newest year first. Passages and data sets stay together on one page.
Tap Show answer, or open the detailed solution (free login). Page 1 of 7.
Start here: the repeating CAT PYQs
Study the mensuration pattern in each CAT PYQ, then practise variations. The 12 selected families contain 31 of the 31 questions tagged Area formulas in the reviewed set.
CAT Mensuration Bible Top 10 PYQ Questions
| Questions | CAT Area Covered |
|---|---|
| First 5 CAT Questions | 67.74% |
| First 10 CAT Questions | 93.55% |
| All 12 CAT Questions | 100% |
Importance of Mensuration each year of CAT exam
| CAT year | Total Mensuration questions | First 6 examples | First 10 examples | All 12 examples | Outside these 12 families | Share of all Quant |
|---|---|---|---|---|---|---|
| 2021 | 8 | 7 | 8 | 8 | 0 | 12.12% |
| 2022 | 6 | 4 | 6 | 6 | 0 | 9.09% |
| 2023 | 6 | 4 | 5 | 6 | 0 | 9.09% |
| 2024 | 6 | 3 | 5 | 6 | 0 | 9.09% |
| 2025 | 5 | 5 | 5 | 5 | 0 | 7.58% |
| Total | 31 | 23 | 29 | 31 | 0 | 9.39% |
| Share of all 31 | 100% | 74.19% | 93.55% | 100% | 0% |
Quick review for beginners and last day revision
| Rule | Formula or what to do | Small example |
|---|---|---|
| Triangle | Area = base × perpendicular height / 2 | A = bh/2 |
| Same altitude | Triangles with the same height have areas in the ratio of their bases. | Area ABD : area ADC = BD : DC |
| Similar figures | Area ratio = square of the corresponding length ratio. | Side ratio 1 : 2 → area ratio 1 : 4. |
| Rectangle and square | Rectangle = length × breadth; square = side² | For square diagonal d, area = d²/2. |
| Parallelogram | Area = base × height = ab sin θ | Use the included angle between sides a,b. |
| Trapezium | Area = (sum of parallel sides) × height / 2 | A = (a + b)h/2 |
| Rhombus | Area = d₁d₂/2 | Diagonals bisect at right angles. |
| Circle and sector | Circle = πr²; sector = (θ/360)πr² when θ is in degrees. | A segment is sector area minus the corresponding triangle area. |
| Equilateral triangle | Area = √3·s²/4; height = √3·s/2 | A regular hexagon is six equilateral triangles. |
| Inradius | Triangle area = inradius × semiperimeter. | For a right triangle, r = (leg₁ + leg₂ − hypotenuse)/2. |
10 Core CAT PYQ Questions
Study these first.
CAT PYQ 1: Common heights midpoints and triangle area ratios
Understand: Triangles that share an angle or a height have areas in the ratio of their sides or bases. Multiply the ratios.
Answer: 30
Solution — first steps
Step 2. Triangles ADE and ABC have the same included angle at A.
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CAT PYQ 2: Rhombus diagonals side and area
Understand: The diagonals of a rhombus cross at right angles, so the half-diagonals and the side form a right triangle.
Answer: A. \(\sqrt{37} + \sqrt{13}\)
Solution — first steps
Step 2. Half-diagonals and side 5 form right triangles, so p²+q²100.
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CAT PYQ 3: Regular polygon decomposition and area
Understand: A regular polygon is made of equal triangles. Count them and use the area of one triangle.
Answer: D. \(2\sqrt{6}\)
Solution — first steps
Step 2. The equilateral triangle area is(√3/4)×12².
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CAT PYQ 4: Trapezium area after finding height
Understand: Find the height from the perimeter and the right triangle on the slanting side, then use the trapezium formula.
Answer: 66
Solution — first steps
Step 2. Perimeter 36 gives h+√(h²+25)=25.
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CAT PYQ 5: Right triangle incircle and area
Understand: In a right triangle, inradius = (leg + leg − hypotenuse)/2. Use it with Pythagoras to find the missing side.
Answer: 120
Solution — first steps
Step 2. Right-triangle relation r=(10+b−c)/2 gives c=b+2.
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CAT PYQ 7: Circle sectors segments and overlapping regions
Understand: Find the angle each arc covers. Add sector areas and subtract triangles to get the overlap.
Answer: C. 32(π − 1)
Solution — first steps
Step 2. The first disk radius 4√2 has area 32π. Its chord BC bounds a semicircle on A side.
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CAT PYQ 9: Parallelogram area from angle and diagonal
Understand: Use the cosine rule to find the unknown side, then area = ab sin θ.
Answer: B. \(25(\sqrt{3} + \sqrt{15})\)
Solution — first steps
Step 2. Cosine rule in triangle ADC: 20²=10²+L²−20L cos 30°.
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CAT PYQ 10: Rectangle on a circle from perimeter and diameter
Understand: The diagonal of a rectangle inside a circle is the diameter. Use the sum of sides and the sum of squares to get the product.
Answer: B. \(\dfrac{P^{2}}{8} - 2R^{2}\)
Solution — first steps
Step 2. The perimeter gives u+v=P/2.
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Answer: 60
Solution — first steps
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Answer: A. 20(3 + √14)
Solution — first steps
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Then, the ratio of the areas of trapezium PBCQ and hexagon ABCDEF is _______
Answer: 5 : 24
Solution — first steps
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Answer: 126
Solution — first steps
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Answer: A. 48
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Frequently asked questions
Where can I find CAT mensuration questions with solutions?
Every Mensuration question on this page is a real CAT question from the CAT Actual Quant Papers. Tap Show answer for the answer; the detailed step-by-step solution opens after a free login. Start with the 12 CAT PYQs at the top, because they repeat the most.
Are there CAT mensuration questions with answers?
Yes. Every question has its answer one tap away, free for everyone: pick an option and press Submit, or tap Show answer.
Is there a PDF of CAT mensuration questions?
Yes. Tap Download PDF at the top of this page (free, after a quick OTP login) for the CAT Mensuration Bible Top 10 PYQ Questions, a free PDF of the 10 most repeated CAT mensuration questions. All the CAT Mensuration questions are also on this page to read online, with answers and, after a free login, detailed solutions.
What are the CAT mensuration previous year questions (PYQs)?
They are the real questions of the CAT Actual Quant Papers that are about mensuration: 31 questions, grouped into 12 repeating CAT PYQs, with the other questions listed after them in paper order.
Which mensuration questions should I practise first for CAT?
Start with the first 6 CAT PYQs, which cover about 70% of the Mensuration questions. Then do the first 10 (about 90%) and finally all 12 (all of them).
How many Mensuration questions came in CAT papers?
19 Mensuration questions are on this page: 5 in CAT 2025, 5 in CAT 2024, 4 in CAT 2023, 3 in CAT 2022, 2 in CAT 2021. The same real question is shown once.
How difficult are CAT Mensuration questions?
Of the 5 Mensuration questions that carry a difficulty rating, 0 are Easy, 4 Medium and 1 Hard; the other 14 are not rated yet.
Are the solutions free?
The question and its answer are free for everyone. The detailed Cetking solution opens after a free login with your mobile number (OTP).
How is a set shown on this page?
Each passage or data set gets one page with all its questions together (1 set here), so you never solve half of one. Questions that stand alone are shown five to a page.
Where can I practise more Mensuration?
Open all CAT papers and topics for every paper, or the Cetking Arena to practise.
Last day solving checklist
- Name the unknown. Include its unit and state whether it is a count, amount, rate or parameter.
- Form the relationships. Translate each given condition into an equation or restriction.
- Choose the method. Use the formula, substitution, elimination, a sign chart or a bound appropriate to this concept.
- Check restrictions. Check integer counts, signs, nonzero denominators, domains and all original conditions.
- Verify the answer. Substitute into the original question; for an extreme, show a feasible example reaches it.
All 12 repeating CAT PYQs and how much each adds
| CAT PYQ | Repeating CAT PYQ | Questions | Representative | Cumulative questions | Cumulative share |
|---|---|---|---|---|---|
| 1 | Common heights midpoints and triangle area ratios | 10 | CAT 2021 S2 Q11 | 10 | 32.26% |
| 2 | Rhombus diagonals side and area | 3 | CAT 2021 S2 Q9 | 13 | 41.94% |
| 3 | Regular polygon decomposition and area | 3 | CAT 2021 S1 Q6 | 16 | 51.61% |
| 4 | Trapezium area after finding height | 3 | CAT 2022 S1 Q11 | 19 | 61.29% |
| 5 | Right triangle incircle and area | 2 | CAT 2021 S1 Q14 | 21 | 67.74% |
| 6 | Rectangle area constraint and optimisation | 2 | CAT 2021 S3 Q19 | 23 | 74.19% |
| 7 | Circle sectors segments and overlapping regions | 2 | CAT 2022 S3 Q18 | 25 | 80.65% |
| 8 | Area of a region defined by coordinate equations | 2 | CAT 2023 S2 Q19 | 27 | 87.10% |
| 9 | Parallelogram area from angle and diagonal | 1 | CAT 2021 S3 Q11 | 28 | 90.32% |
| 10 | Rectangle on a circle from perimeter and diameter | 1 | CAT 2022 S1 Q19 | 29 | 93.55% |
| 11 | Right triangle on a diameter and proportional legs | 1 | CAT 2023 S2 Q18 | 30 | 96.77% |
| 12 | Cuboid surface area and sphere diameter | 1 | CAT 2024 S1 Q16 | 31 | 100% |
Based on CAT Actual Quant Papers.