Mensuration – Quick Study Guide
(For the Meghalaya Forest Guard Quantitative Aptitude Paper)
1. What is Mensuration?
Mensuration is the part of math that deals with figures, shapes, and surfaces.
It tells you how to find:
- Area – the flat space inside a shape.
- Perimeter – the distance around a shape.
- Volume – the space inside a 3‑D object.
Think of it like measuring a garden:
Area = how much ground you can plant on.
Perimeter = how long a fence you need.
Volume = how many water‑buckets can fit inside a water‑tank.
2. Handy Rules (No Jargon)
| Shape | Area Formula | Perimeter Formula | Volume Formula |
|---|---|---|---|
| Rectangle / Square | length × breadth | 2 × (length + breadth) | – |
| Triangle | ½ × base × height | a + b + c (add all sides) | – |
| Circle | π × radius² | 2 × π × radius | – |
| Parallelogram | base × height | 2 × (base + height) | – |
| Trapezium | ½ × (sum of parallel sides) × height | a + b + c + d | – |
| Cube | 6 × side² | 12 × side | side³ |
| Cuboid (rectangular box) | 2 × (ab + bc + ca) | 4 × (a + b + c) | a × b × c |
| Sphere | – | 4 × π × radius² | 4/3 × π × radius³ |
| Cylinder | π × r² + 2 × π × r × h | 2 × π × r + 2 × π × (r + h) | π × r² × h |
| Cone | π × r² + π × r × slant | 2 × π × (r + slant) | 1/3 × π × r² × h |
π ≈ 3.1416
slant = slant height of the cone (the slanted side, not the vertical height)
3. Quick Tips
- Always find the “base” and “height” first – most area formulas use them.
- Use 2 × (a + b) for rectangles, squares, and parallelograms.
- For triangles, remember ½ × base × height – half of a rectangle.
- When you see “π”, you’re dealing with circles, spheres, cylinders, or cones.
- Check units – if area is in sq. meters, perimeter in meters, volume in cubic meters.
- Practice converting between shapes – a cube is just six squares stuck together.
4. Tiny Example
Problem
A rectangular garden is 10 m long and 6 m wide.
How much fencing (perimeter) is needed?
How many 1 m² flower beds can fit inside?
Solution
-
Perimeter
[ P = 2 \times (10 + 6) = 2 \times 16 = 32 \text{ m} ] → 32 m of fence. -
Area
[ A = 10 \times 6 = 60 \text{ m}^2 ] → 60 flower beds of 1 m² each.
5. Practice Problems
- Find the area of a triangle with base 8 cm and height 5 cm.
- A circle has a diameter of 12 m. What is its perimeter (circumference)?
- A cube has side length 4 ft. What is its volume?
- A cylinder has radius 3 m and height 10 m. Find its volume.
(Try solving before looking at the solutions below.)
Answers
| # | Solution |
|---|---|
| 1 | Area = ½ × 8 × 5 = 20 cm² |
| 2 | Circumference = π × diameter = 3.1416 × 12 ≈ 37.7 m |
| 3 | Volume = 4³ = 64 ft³ |
| 4 | Volume = π × 3² × 10 ≈ 3.1416 × 9 × 10 ≈ 282.7 m³ |
6. Final Thought
Mensuration is like having a toolbox for all shapes you see daily—gardens, rooms, animals, trees. Once you know these simple formulas, you can measure almost anything quickly and accurately. Keep practicing, and you'll master it in no time. Good luck with your Forest Guard exam!