Step by step
The question
Question: find the surface area of a box 4 cm long, 3 cm wide and 2 cm high.
1 Count the faces
The surface area is the area of all the outside faces.
A box has 6 faces.
They come in 3 pairs, the same size.
2 Top and bottom
The top is 4 by 3.
Its area is 4 times 3, that is 12.
The bottom is the same.
Two faces of 12: 2 times 12 is 24.
2 × (4 × 3) = 2 × 12 = 24 cm2
3 Front and back
The front is 4 by 2.
Its area is 4 times 2, that is 8.
The face behind it is the same.
Two faces of 8: 2 times 8 is 16.
2 × (4 × 2) = 2 × 8 = 16 cm2
4 The two sides
The side is 3 by 2.
Its area is 3 times 2, that is 6.
The face behind it is the same.
Two faces of 6: 2 times 6 is 12.
2 × (3 × 2) = 2 × 6 = 12 cm2
5 Add all the faces
Add the three pairs: 24 + 16 + 12.
S = 24 + 16 + 12
24 plus 16 is 40.
S = 40 + 12
40 plus 12 is 52.
So the surface area is 52 cm².
S = 52 cm2
Let's look back.
First: count the faces.
Then: top and bottom.
Then: front and back.
Then: the two sides.
Last: add all the faces.
Answer
S = 52 cm2