Area is how much surface a shape covers; volume is how much space a solid fills. Get the units right — area is in square units, volume in cubic ones.
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Every one of these comes from the rectangle. A triangle is half a rectangle; a trapezium is the average of its parallel sides times the height.
⬛ The formulas
| Shape | Area | Perimeter |
|---|---|---|
| Rectangle | l × b | 2(l + b) |
| Square | side² | 4 × side |
| Triangle | ½ × base × height | sum of the three sides |
| Parallelogram | base × height | 2(a + b) |
| Trapezium | ½ × (a + b) × h | sum of the four sides |
| Rhombus | ½ × d₁ × d₂ | 4 × side |
| Circle | πr² | 2πr (circumference) |
Height means perpendicular height, not the slanted side. In a parallelogram or triangle, the height is the straight-down distance from the top to the base — measured at a right angle.
Surface area is the total area of all the faces — what you would need to wrap the solid in paper.
📦 Solids
| Solid | Surface area | Volume |
|---|---|---|
| Cube | 6a² | a³ |
| Cuboid | 2(lb + bh + hl) | l × b × h |
| Cylinder | 2πr(r + h) | πr²h |
Use π = 22/7 when the radius is a multiple of 7 — the sevens cancel and the arithmetic becomes easy. Otherwise 3.14 is usually intended. The question normally tells you which to use.
More marks are lost to units in this chapter than to any formula.
📐 Converting correctly
| Quantity | Unit | Conversion |
|---|---|---|
| Length | cm, m | 1 m = 100 cm |
| Area | cm², m² | 1 m² = 10,000 cm² |
| Volume | cm³, m³ | 1 m³ = 10,00,000 cm³ |
| Capacity | litre | 1 litre = 1000 cm³ |
1 m² is not 100 cm². It is 100 × 100 = 10,000 cm², because both length and width are converted. The same trap gives 1 m³ = 100³ = 10,00,000 cm³.
12 questions on area, surface area and volume. Write the formula before the numbers. 🍀
