Step by step
The question
Question: find the surface area of a cube with sides 6 m.
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 6.
Its area is 6 times 6, that is 36.
The bottom is the same.
Two faces of 36: 2 times 36 is 72.
2 × (6 × 6) = 2 × 36 = 72 m2
3 Front and back
The front is 6 by 6.
Its area is 6 times 6, that is 36.
The face behind it is the same.
Two faces of 36: 2 times 36 is 72.
2 × (6 × 6) = 2 × 36 = 72 m2
4 The two sides
The side is 6 by 6.
Its area is 6 times 6, that is 36.
The face behind it is the same.
Two faces of 36: 2 times 36 is 72.
2 × (6 × 6) = 2 × 36 = 72 m2
5 Add all the faces
Add the three pairs: 72 + 72 + 72.
S = 72 + 72 + 72
72 plus 72 is 144.
S = 144 + 72
144 plus 72 is 216.
So the surface area is 216 m².
S = 216 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 = 216 m2