Discover
To wrap a box you need to cover its outside. Which measure is that?
- Surface area
- Volume
Not to scale
Turn and tilt the box. Count its faces, the hidden ones too.
- 6 faces, in 3 matching pairs
- 4 faces: the ones on the sides
Key idea
Surface area adds the faces.
The surface area of a prism is the sum of the areas of all its faces: two bases plus the side rectangles (perimeter of the base × length). For a box: . Volume is base area × height, in cubic units.
Worked example
A box 5 by 3 by 2.
Not to scale
Pairs of faces.
square units
Add.
Your turn, guided
Your turn: the surface area of a cube with edge 3.
6 · 9.
Practice ★
- Find the surface area of a box (rectangular prism) 6 cm by 9 cm by 5 cm (cm²).Not to scale
- Find the surface area of a box (rectangular prism) 7 cm by 3 cm by 7 cm (cm²).Not to scale
- Find the surface area of a cube with edge 10 cm (cm²).
Watch out!
Practice ★★
- A prism has right-triangle bases with sides 3, 4 and 5 cm, and length 7 cm. Find its surface area (cm²).Not to scale
- A prism has right-triangle bases with sides 9, 12 and 15 cm, and length 2 cm. Find its surface area (cm²).Not to scale
- Boss problem. A gift box is 6 in long, 4 in wide and 5 in tall.
Exit ticket
Three questions to check you have got it.
- Find the surface area of a box (rectangular prism) 6 cm by 9 cm by 5 cm (cm²).Not to scale
- Find the surface area of a box (rectangular prism) 7 cm by 3 cm by 7 cm (cm²).Not to scale
- Find the surface area of a box (rectangular prism) 8 cm by 2 cm by 3 cm (cm²).Not to scale
Summary card
Surface area
Add the areas of all faces (square units).
Watch out: covering is area; filling is volume.