Area, Perimeter and Volume Formulas
The essential formulas for common 2D and 3D shapes, with units and a worked example.
Key concept
Perimeter is the distance around a 2D shape. Area is the amount of surface it covers. Volume is the space inside a 3D shape. Perimeter is measured in units of length (cm, m), area in square units (cm², m²), and volume in cubic units (cm³, m³).
Formulas
| Shape | Perimeter | Area |
|---|---|---|
| Rectangle (length l, width w) | 2l + 2w | l × w |
| Square (side s) | 4s | s² |
| Triangle (base b, height h) | sum of sides | ½ × b × h |
| Parallelogram | sum of sides | b × h |
| Trapezium (parallel sides a, b, height h) | sum of sides | ½ × (a + b) × h |
| Circle (radius r) | circumference = 2πr | πr² |
| Solid | Volume |
|---|---|
| Cuboid | l × w × h |
| Cylinder (radius r, height h) | πr²h |
| Cone | ⅓ × πr²h |
| Sphere | (4/3)πr³ |
| Prism | cross-section area × length |
Worked example 1: circle
A circle has radius 5 cm. Find its circumference and area, using π ≈ 3.14.
- Circumference = 2 × 3.14 × 5 = 31.4 cm.
- Area = 3.14 × 5² = 3.14 × 25 = 78.5 cm².
Worked example 2: cylinder
A cylinder has radius 3 cm and height 10 cm. Use π ≈ 3.14.
- Volume = 3.14 × 3² × 10 = 3.14 × 9 × 10 = 282.6 cm³.
Common mistakes
- Mixing units, such as cm with m.
- Using the diameter instead of the radius. The radius is half the diameter.
- Using the slant height instead of the perpendicular height in a triangle.
- Writing area in cm instead of cm².
Quick recap
Learn the table, check units, and identify the radius before substituting.