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Mensuration is pure formula application — the questions are usually direct, so this chapter is about building a reliable formula sheet, not tricks.
| Shape | Area | Perimeter |
|---|---|---|
| Square (side a) | a² | 4a |
| Rectangle (l, b) | l × b | 2(l + b) |
| Triangle (base b, height h) | ½ × b × h | sum of sides |
| Circle (radius r) | πr² | 2πr (circumference) |
| Shape | Volume | Total Surface Area |
|---|---|---|
| Cube (side a) | a³ | 6a² |
| Cuboid (l, b, h) | l × b × h | 2(lb + bh + hl) |
| Cylinder (r, h) | πr²h | 2πr(h + r) |
| Sphere (r) | (4/3)πr³ | 4πr² |
Find the area of a rectangle with length 12 cm and breadth 7 cm.
Area = 12 × 7 = 84 cm².
Find the volume of a cube with side 5 cm.
Volume = 5³ = 125 cm³.
Find the curved surface area of a cylinder with radius 7 cm and height 10 cm (use π = 22/7).
CSA = 2πrh = 2 × (22/7) × 7 × 10 = 440 cm².
Watch for total surface area vs. curved/lateral surface area — exams often ask for one specifically, and using the wrong formula is a very common slip.
1. Find the area of a rectangle with length 15 cm and breadth 8 cm.
2. Find the volume of a cube with side 4 cm.
3. What is the circumference of a circle with radius 7 cm? (use π = 22/7)