Learning Objectives
- explain surface area as the total outside area of a solid;
- identify faces of cubes, cuboids, prisms and cylinders;
- use nets to understand surface area;
- calculate total surface area;
- solve missing-dimension problems.
Introduction
This lesson develops Surface Area from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
Visual Exploration
Use the diagrams, tables or examples in this lesson to identify what changes, what stays fixed and which relationship connects the values.
What Is Surface Area?
Surface area is the total area of every exposed face of a three-dimensional object.
Net of a Cuboid
Useful Formulas
Worked Example: Cuboid
Find the surface area of a cuboid 8 cm by 5 cm by 3 cm.
lw = 8×5 = 40.
lh = 8×3 = 24.
wh = 5×3 = 15.
SA = 2(40+24+15)=158 cm².
Open Containers
If a box has no lid, do not include the missing top face.
🧠 Let’s Think Together
Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.
Practice Questions
Foundation- Find the surface area of a cube with side 6 cm.
- Find the surface area of a cuboid 10 cm by 4 cm by 3 cm.
- A cube has surface area 150 cm². Find its side length.
- Find the area of cardboard needed for an open box 12 cm by 8 cm by 5 cm.
- A cuboid has dimensions 9 cm by 6 cm by h cm and surface area 300 cm². Find h.
- Two cubes of side 4 cm are joined face-to-face. Find the surface area of the new solid.
✅ Check Your Work
Show practice answers
- 6×36=216 cm².
- 2(40+30+12)=164 cm².
- 6s²=150, so s²=25 and s=5 cm.
- Base 96 + two 12×5 faces + two 8×5 faces = 296 cm².
- 2(54+9h+6h)=300 → 108+30h=300 → h=6.4 cm.
- Two separate cubes have 192 cm², but the two joined faces become internal: 192−32=160 cm².
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Surface area is the total exposed outer area.
- Nets help reveal all faces.
- Missing or joined faces must not be counted.