Mensuration Formula Sheet: 2D and 3D Shapes for SSC and Banking
All the area, perimeter, surface area and volume formulas you need for exams, with a worked example for each shape and the common traps.
By the World MCQ Forum India Editorial Team · 27 October 2026 · 3 min read
Mensuration questions are almost always direct: pick the right formula, put in the numbers, calculate. This page lists every formula you need, in the order exams usually test them. Unless a question says otherwise, take π = 22/7 and choose radii that are multiples of 7 to make the arithmetic easy.
Plane figures (2D)
| Shape | Perimeter | Area |
|---|---|---|
| Rectangle (l, b) | 2(l + b) | l × b |
| Square (side a) | 4a | a², or (diagonal)² ÷ 2 |
| Triangle (base b, height h) | sum of sides | ½ × b × h |
| Triangle (sides a, b, c) | a + b + c | √[s(s − a)(s − b)(s − c)], where s = (a + b + c) ÷ 2 |
| Equilateral triangle (side a) | 3a | (√3 ÷ 4) × a² |
| Rhombus (diagonals d₁, d₂) | 4 × side | ½ × d₁ × d₂ |
| Trapezium (parallel sides a, b; height h) | sum of sides | ½ × (a + b) × h |
| Circle (radius r) | 2πr | πr² |
| Semicircle (radius r) | πr + 2r | ½πr² |
Worked example (Heron’s formula): sides 13, 14 and 15 cm. s = 21, so the area is √(21 × 8 × 7 × 6) = √7056 = 84 cm².
Rhombus side: its diagonals cut each other at right angles, so side = √[(d₁/2)² + (d₂/2)²]. With diagonals 12 and 16: √(36 + 64) = 10 cm.
Solid figures (3D)
| Solid | Curved / lateral surface | Total surface area | Volume |
|---|---|---|---|
| Cuboid (l, b, h) | 2h(l + b) (four walls) | 2(lb + bh + hl) | l × b × h |
| Cube (side a) | 4a² | 6a² | a³ |
| Cylinder (r, h) | 2πrh | 2πr(r + h) | πr²h |
| Cone (r, h, slant l) | πrl | πr(r + l) | ⅓πr²h |
| Sphere (r) | — | 4πr² | ⁴⁄₃πr³ |
| Hemisphere (r) | 2πr² | 3πr² | ⅔πr³ |
Useful extras:
- Diagonal of a cube = a√3; diagonal of a face = a√2.
- Diagonal of a cuboid = √(l² + b² + h²).
- Slant height of a cone l = √(r² + h²).
- A cone holds exactly one-third of a cylinder with the same base and height.
Scaling: what happens when dimensions change
| Change | Effect on area | Effect on volume |
|---|---|---|
| Every length doubled | × 4 | × 8 |
| Every length tripled | × 9 | × 27 |
| Every length up 20% | up 44% (1.2² = 1.44) | up 72.8% (1.2³ = 1.728) |
Wheel and distance questions
Distance covered in one revolution = circumference = 2πr.
Example: a wheel of radius 35 cm has a circumference of 2 × 22/7 × 35 = 220 cm. To cover 2.2 km (2,20,000 cm) it makes 2,20,000 ÷ 220 = 1,000 revolutions.
Common traps
- Units: convert everything to the same unit before calculating. 1 m = 100 cm, but 1 m² = 10,000 cm² and 1 m³ = 10,00,000 cm³. Also, 1 litre = 1,000 cm³.
- Hemisphere total surface includes the flat circle: 3πr², not 2πr².
- Four walls of a room use 2h(l + b); the floor and ceiling are not included.
- Semicircle perimeter includes the diameter: πr + 2r, not just πr.
Practise every formula in our mensuration set. All its answers were calculated by script.