Step by step
The question
Question: draw the net of a box 5 by 2 by 1, and find its surface area.
box 5 by 2 by 1
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: 5 × 2 is 10.
= top and bottom: 5 × 2 = 10
Front and back: 5 × 1 is 5.
= front and back: 5 × 1 = 5
The two sides: 2 × 1 is 2.
= the two sides: 2 × 1 = 2
Careful!
Count every face in the net.
A box has 6 faces, not 3.
Careful: not 10 + 5 + 2 = 17 ✗
3 Add them all
We add all 6 faces: 34.
= SA = 10 + 10 + 5 + 5 + 2 + 2 = 34
4 Check
Let's check another way.
The faces come in pairs.
One of each: 10 plus 5 plus 2 is 17.
Times 2 is 34.
So the answer is right!
2 × (10 + 5 + 2) = 2 × 17 = 34
Let's look back.
First: unfold it.
Then: area of each face.
Then: add them all.
Last: check.
Answer
= SA = 10 + 10 + 5 + 5 + 2 + 2 = 34