Step by step
The question
Question: draw the net of a box 8 m by 3 m by 2 m, and find its surface area.
box 8 m by 3 m by 2 m
The surface area is the area of all the outside faces together.
A net shows every face flat.
surface area = all the faces added
1 Unfold it
We cut along some edges and fold it flat.
Matching faces have the same colour.
2 Area of each face
Top and bottom: 8 × 3 is 24.
= top and bottom: 8 × 3 = 24
Front and back: 8 × 2 is 16.
= front and back: 8 × 2 = 16
The two sides: 3 × 2 is 6.
= the two sides: 3 × 2 = 6
Careful!
Count every face in the net.
A box has 6 faces, not 3.
Careful: not 24 + 16 + 6 = 46 ✗
3 Add them all
We add all 6 faces: 92 m².
= SA = 24 + 24 + 16 + 16 + 6 + 6 = 92 m²
4 Check
Let's check another way.
The faces come in pairs.
One of each: 24 plus 16 plus 6 is 46.
Times 2 is 92.
So the answer is right!
2 × (24 + 16 + 6) = 2 × 46 = 92
Let's look back.
First: unfold it.
Then: area of each face.
Then: add them all.
Last: check.
Answer
= SA = 24 + 24 + 16 + 16 + 6 + 6 = 92 m²