Step by step
The question
Question: find the surface area of a box 6 m long, 3 m wide and 1 m 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 6 by 3.
Its area is 6 times 3, that is 18.
The bottom is the same.
Two faces of 18: 2 times 18 is 36.
2 × (6 × 3) = 2 × 18 = 36 m2
3 Front and back
The front is 6 by 1.
Its area is 6 times 1, that is 6.
The face behind it is the same.
Two faces of 6: 2 times 6 is 12.
2 × (6 × 1) = 2 × 6 = 12 m2
4 The two sides
The side is 3 by 1.
Its area is 3 times 1, that is 3.
The face behind it is the same.
Two faces of 3: 2 times 3 is 6.
2 × (3 × 1) = 2 × 3 = 6 m2
5 Add all the faces
Add the three pairs: 36 + 12 + 6.
S = 36 + 12 + 6
36 plus 12 is 48.
S = 48 + 6
48 plus 6 is 54.
So the surface area is 54 m².
S = 54 m2
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 = 54 m2