Area, Perimeter, Volume and Surface Area
Perimeter, area, volume and surface area
- Perimeter = the total distance around the edge of a 2D shape (add up all the sides), measured in units (cm, m).
- Area = the space inside a 2D shape, in square units (cm², m²).
- Volume = the space inside a 3D solid, in cubic units (cm³, m³).
- Surface area = the total area of all the faces of a 3D solid, in square units.
Area formulas (learn these)
| Shape | Area |
|---|---|
| Rectangle | length × width |
| Triangle | ½ × base × height |
| Parallelogram | base × height |
| Trapezium | ½ × (a + b) × height |
| Circle | π r² |
Circle circumference (perimeter): C = π × d = 2 π r.
Volume formulas
| Solid | Volume |
|---|---|
| Cuboid | length × width × height |
| Prism (any) | area of cross-section × length |
| Cylinder | π r² × height |
| Cone | ⅓ × π r² × height |
| Sphere | ⁴⁄₃ π r³ |
A prism has the same cross-section all the way through — its volume is always cross-section area × length.
Surface area
Add up the area of every face. For solids with curved surfaces:
- Cylinder surface area = 2πr² (two circles) + 2πrh (curved side).
- A net (the shape unfolded flat) helps you see all the faces.
Working with circles
- Learn area = πr² and circumference = πd. Don't mix them up (area uses r squared).
- For a semicircle, halve the circle's area; for arcs/sectors, take the correct fraction of the circle.
Worked example
Find the area of a circle with radius 5 cm (take π = 3.14).
area = π r² = 3.14 × 5² = 3.14 × 25 = 78.5 cm²✓
Common mistakes
- Confusing area (πr²) with circumference (πd) of a circle.
- Forgetting to use the radius (half the diameter) in circle formulas.
- Mixing up units — area is squared, volume is cubed.
- Only adding some faces when finding surface area.
Exam tips
- Learn the key formulas; some are given but circle and prism ones you should know.
- Always include the correct units (cm² for area, cm³ for volume).
- For a prism, find the cross-section area first, then × length.
Key facts to remember
- Perimeter = around; area = inside (units²); volume = inside a solid (units³); surface area = all faces added.
- Circle: area = πr², circumference = πd = 2πr.
- Prism volume = cross-section area × length; cylinder = πr²h.