Surface area of a cuboid and a cube

Surface area of a cuboid and a cube

Surface area of a cuboid and a cube

Surface area is the total area of all the faces of a solid. We measure it in square units (cm², m², …).

Cuboid

A cuboid has 6 faces, with opposite pairs being identical. The edges are `a`, `b`, `c`.

SA = 2(ab + bc + ac)

Example. A cuboid with `a = 5 cm`, `b = 4 cm`, `c = 3 cm`:

SA = `2 · (5·4 + 4·3 + 5·3) = 2 · (20 + 12 + 15) = 2 · 47 = 94 cm²`.

Cube

A cube is a special cuboid with all edges equal (`a = b = c`).

SA = 6 · a²

Example. A cube with edge 5 cm: SA = `6 · 5² = 6 · 25 = 150 cm²`.

Step by step

  1. Compute the areas of the three pairs of faces: `ab`, `bc`, `ac`.
  2. Multiply by 2 (each pair appears twice).
  3. Add the results.

Common pitfalls

  • Edges in the same unit. If one is in cm and another in dm, convert first.
  • Don't forget to multiply by 2. The formula has a 2 at the front.
  • The unit of surface area is always square (cm², m²), not cubic.

Try it yourself