CAT Mensuration Bible Top 10 Must Solve Mensuration Questions covering 90% of Syllabus – Page 4
All 19 Mensuration questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 4 of 7.
Refer to the passage above ↑
The length of each side of an equilateral triangle ABC is 3 cm. Let D be a point on BC such that the area of triangle ADC is half the area of triangle ABD. Then the length of AD, in cm, is
Answer: C. √7
Solution — first steps
Step 1. Same altitude gives DC: BD=1: 2, so DC 1 and BD 2.
Step 2. Take B=(0, 0), C=(3, 0), A=(1.5, 3√3/2), D=(2, 0).
Step 2. Take B=(0, 0), C=(3, 0), A=(1.5, 3√3/2), D=(2, 0).
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
Refer to the passage above ↑
In triangle ABC, altitudes AD and BE are drawn to the corresponding bases. If ∠BAC = 45° and ∠ABC = θ, then AD/BE equals
Answer: D. √2 sin θ
Solution — first steps
Step 1. Equal triangle area gives BC×AD=AC×BE.
Step 2. Thus AD/BE=AC/BC.
Step 2. Thus AD/BE=AC/BC.
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
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.