📚 Mensuration – Quick & Easy Study Notes
(For Haryana Police Constable – Quantitative Aptitude)
1️⃣ What is Mensuration?
- Mensuration = finding sizes of shapes.
- Think of it as measuring a room – how big is the floor? how long is the wall?
2️⃣ Key Ideas (No fancy words!)
| Idea | Everyday Analogy | What to Do |
|---|---|---|
| Area | How many square tiles fit on a floor | Multiply the size of one tile by the number of tiles |
| Perimeter | How long the fence around a garden is | Add the lengths of all sides |
| Volume | How much water a box can hold | Multiply length × width × height |
| Surface Area | How much paint is needed for a box | Add the areas of all its sides |
3️⃣ Simple Shapes – Formulas + Tiny Example
| Shape | Formula (short) | Tiny Example |
|---|---|---|
| Rectangle | Area = length × width Perimeter = 2 × (length + width) |
A 4 m × 3 m room → Area = 4 × 3 = 12 m² |
| Square | Area = side² Perimeter = 4 × side |
5 m side → Area = 5² = 25 m² |
| Triangle | Area = ½ × base × height | Base 6 m, height 4 m → ½ × 6 × 4 = 12 m² |
| Circle | Area = π × radius² Perimeter (Circumference) = 2 × π × radius |
Radius 3 m → Area ≈ 28.3 m² |
| Parallelogram | Area = base × height | Base 5 m, height 3 m → 15 m² |
| Trapezium (Trapezoid) | Area = ½ × (sum of parallel sides) × height | Bases 4 m & 6 m, height 3 m → ½ × (4+6) × 3 = 15 m² |
| Cube | Volume = side³ Surface Area = 6 × side² |
Side 2 m → Volume = 8 m³, Surface Area = 24 m² |
| Rectangular Box (Cuboid) | Volume = length × width × height Surface Area = 2 × (lw + lh + wh) |
3 m × 2 m × 1.5 m → Volume = 9 m³, Surface Area = 30 m² |
(Use π ≈ 3.14 or 22/7 when needed.)
4️⃣ Quick Tips (No jargon)
- Always check units – cm, m, km, etc.
- Keep it simple – If you can’t remember a formula, break the shape into squares or rectangles.
- Use a ruler – For real‑life problems, measure first, then calculate.
- Round carefully – If the answer asks for “nearest whole number”, round 0.5 up.
5️⃣ Tiny “Practice” Problems
| # | Question | Quick Work‑Through | Answer |
|---|---|---|---|
| 1 | A garden is a rectangle 8 m long and 5 m wide. How many tiles (1 m² each) are needed? | Area = 8 × 5 = 40 | 40 tiles |
| 2 | A fence surrounds a square field 10 m on each side. What is the fence length? | Perimeter = 4 × 10 = 40 | 40 m |
| 3 | A box 2 m × 1.5 m × 1 m holds water. How much water (in m³) can it hold? | Volume = 2 × 1.5 × 1 = 3 | 3 m³ |
| 4 | A pizza is a circle with radius 10 cm. Find its area (π = 3.14). | Area = 3.14 × 10² = 3.14 × 100 = 314 | 314 cm² |
| 5 | A trapezium has parallel sides 4 m and 7 m, height 3 m. What is its area? | Area = ½ × (4+7) × 3 = ½ × 11 × 3 = 16.5 | 16.5 m² |
6️⃣ Quick Checklist Before You Write an Answer
- Identify the shape – rectangle, circle, etc.
- Write the formula – area, perimeter, volume.
- Insert the numbers – keep units consistent.
- Do the math – use a calculator if needed.
- Check the answer – does it make sense? (e.g., area of a 2 m × 2 m square can’t be 10 m²)
7️⃣ Why It Matters for the Constable Exam
- Speed & Accuracy – most questions are straight‑forward calculations.
- Logical Thinking – breaking shapes into simpler parts shows you understand geometry.
- Confidence – knowing the basics helps you avoid silly mistakes.
🎉 Final Thought
Think of mensuration like packing a suitcase: you need to know how much space each item takes (area, volume) and how much border you’ll add (perimeter). Once you get the hang of it, the numbers just line up!