Surface Area from Nets

A solid can be unfolded flat. The flat pattern is called a net.

Net is a flat pattern that folds up into a solid.

Surface area is the total

Work out the area of every face on the net, then add them all up.

Faces come in pairs

A box has three pairs of matching faces, so work out three and double each.

Not the same as volume

Surface area covers the outside in square units. Volume fills the inside in cubic units.

A net is the solid unfolded

Cut a box along its edges and flatten it and you get a net — all six faces laid out. Surface area is the total area of the net, so the three-dimensional problem becomes an ordinary two-dimensional one.

Account for every face

A cuboid has 6 faces in 3 matching pairs. Find the area of one of each pair, double it, and add: 2(lw + lh + wh). Listing the faces before calculating is what stops a face being missed or counted twice.

Surface area and volume answer different questions

Surface area is how much material wraps the outside, measured in square units. Volume is how much space is inside, in cubic units. Wrapping a present is surface area; filling it is volume. The units tell you which you calculated.

Where surface area matters

Packaging design, painting a room, tiling, and heat loss from a building are all surface area problems. It is genuinely the quantity that decides how much material is needed, which is why manufacturers care about it as much as volume.