Mensuration – Essential Study Notes
(Andaman & Nicobar Islands TET – Quantitative Aptitude)
1. Simple Explanation
Mensuration is the branch of mathematics that deals with the measurement of geometric figures.
- Linear measurement – length, perimeter
- Area – 2‑dimensional figures
- Volume – 3‑dimensional figures
In TET exams you’ll be asked to compute perimeters, areas, surface areas, and volumes of the most common shapes.
The key to success is memorizing the fundamental formulas and practising unit conversions.
2. Key Points & Formulas
| Figure | Perimeter / Surface | Area | Volume (if solid) |
|---|---|---|---|
| Square | (P = 4a) | (A = a^2) | – |
| Rectangle | (P = 2(l+w)) | (A = l \times w) | – |
| Parallelogram | (P = 2(a+b)) | (A = b \times h) | – |
| Rhombus | (P = 4a) | (A = \frac{d_1 d_2}{2}) or (A = a \times h) | – |
| Trapezium (Trapezoid) | (P = a+b+c+d) (sum of all sides) | (A = \frac{(a+b)}{2}\times h) | – |
| Circle | (C = 2\pi r) | (A = \pi r^2) | – |
| Ellipse | (C \approx \pi \sqrt{2(a^2+b^2)}) (approx.) | (A = \pi a b) | – |
| Triangle | (P = a+b+c) | (A = \frac{1}{2} \times \text{base} \times \text{height}) | – |
| Sphere | – | – | (V = \frac{4}{3}\pi r^3) |
| Cylinder | (SA = 2\pi r(h+r)) | – | (V = \pi r^2 h) |
| Cone | (SA = \pi r(r + \sqrt{h^2+r^2})) | – | (V = \frac{1}{3}\pi r^2 h) |
| Right Circular Prism | (SA = 2B + P \times h) | Base area (B) | (V = B \times h) |
| Right Circular Pyramid | (SA = B + P \times l) | Base area (B) | (V = \frac{1}{3}B \times h) |
Notes
- (a,b,c,d) – side lengths.
- (h) – height (altitude).
- (r) – radius.
- (l) – slant height (cone/pyramid).
- (P) – perimeter of the base.
- (B) – area of the base.
- For rectangular/triangular prisms/pyramids, (B) is simply the area of that base.
3. Worked Example
Problem
A right circular cylinder has a radius of (5,\text{cm}) and a height of (12,\text{cm}).
Find:
- The lateral surface area (LSA).
- The total surface area (TSA).
- The volume.
Solution
-
Lateral Surface Area
[ \text{LSA} = 2\pi r h = 2\pi (5)(12) = 120\pi , \text{cm}^2 ] -
Total Surface Area
[ \text{TSA} = 2\pi r^2 + 2\pi r h = 2\pi (5)^2 + 120\pi = 50\pi + 120\pi = 170\pi , \text{cm}^2 ] -
Volume
[ V = \pi r^2 h = \pi (5)^2 (12) = 300\pi , \text{cm}^3 ]
Numeric Answers (using (\pi \approx 3.14))
- LSA ≈ (120 \times 3.14 = 376.8 , \text{cm}^2)
- TSA ≈ (170 \times 3.14 = 533.8 , \text{cm}^2)
- Volume ≈ (300 \times 3.14 = 942 , \text{cm}^3)
4. Quick Revision Summary
| Shape | Perimeter/Surface | Area | Volume | Key Formula |
|---|---|---|---|---|
| Square | (4a) | (a^2) | – | – |
| Rectangle | (2(l+w)) | (lw) | – | – |
| Parallelogram | (2(a+b)) | (bh) | – | – |