Step by step
The question
Question: draw the net of a box 2 cm by 2 cm by 5 cm, and find its surface area.
box 2 cm by 2 cm by 5 cm
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: 2 × 2 is 4.
= top and bottom: 2 × 2 = 4
Front and back: 2 × 5 is 10.
= front and back: 2 × 5 = 10
The two sides: 2 × 5 is 10.
= the two sides: 2 × 5 = 10
Careful!
Count every face in the net.
A box has 6 faces, not 3.
Careful: not 4 + 10 + 10 = 24 ✗
3 Add them all
We add all 6 faces: 48 cm².
= SA = 4 + 4 + 10 + 10 + 10 + 10 = 48 cm²
4 Check
Let's check another way.
The faces come in pairs.
One of each: 4 plus 10 plus 10 is 24.
Times 2 is 48.
So the answer is right!
2 × (4 + 10 + 10) = 2 × 24 = 48
Let's look back.
First: unfold it.
Then: area of each face.
Then: add them all.
Last: check.
Answer
= SA = 4 + 4 + 10 + 10 + 10 + 10 = 48 cm²