Surface Area of Solids
Find the surface area of prisms and pyramids by unfolding them into nets of rectangles and triangles, working out each face's area and summing them; apply this to practical problems like wrapping boxes or painting walls
What a learner can do afterwards
- Draw or identify the net of a cuboid, prism, or pyramid and label the dimensions of each face
- Calculate the area of every face and add them to find the total surface area (e.g., a 3 cm × 4 cm × 5 cm box)
- Solve a practical surface-area problem (e.g., how much card is needed to build a model, with the right units)
The lesson
Surface area is the total area of every face on the outside of a solid, like a prism or a pyramid. To find it, imagine unfolding the solid flat into its net. Each face becomes a simple shape, a rectangle or a triangle, and you already know how to find the area of those.
Take a box that is 3 cm by 4 cm by 5 cm. Unfolded, it has three pairs of matching rectangles: 3 cm x 4 cm, 3 cm x 5 cm, and 4 cm x 5 cm. Their areas are 12 cm2, 15 cm2, and 20 cm2. Since each shape appears twice, the total surface area is 2 x (12 + 15 + 20) = 94 cm2.
Always check you have counted every face, including the ones you cannot see, like the bottom and the back. Keep your units the same throughout, such as all in cm2, so nothing gets mixed up.
Unfold the solid, find the area of each face, and add them all together in matching units.
Watch it
Where it sits
This opens up
Nothing builds on it yet.
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.