Worked examples
The question
Question: draw the net of a box 4 by 3 by 2, and find its surface area.
box 4 by 3 by 2
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: 4 × 3 is 12.
= top and bottom: 4 × 3 = 12
Front and back: 4 × 2 is 8.
= front and back: 4 × 2 = 8
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 12 + 8 + 6 = 26 ✗
3 Add them all
We add all 6 faces: 52.
= SA = 12 + 12 + 8 + 8 + 6 + 6 = 52
4 Check
Let's check another way.
The faces come in pairs.
One of each: 12 plus 8 plus 6 is 26.
Times 2 is 52.
So the answer is right!
2 × (12 + 8 + 6) = 2 × 26 = 52
Let's look back.
First: unfold it.
Then: area of each face.
Then: add them all.
Last: check.
Answer = SA = 12 + 12 + 8 + 8 + 6 + 6 = 52
▶ Watch it solved
The question
Question: draw the net of a triangular prism, sides 3, 4, 5, length 10, and find its surface area.
triangular prism, sides 3, 4, 5, length 10
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
Flat: three rectangles in a row, and a triangle at each end.
2 Area of each face
The two triangles: half × 3 × 4 is 6.
= the two triangles: ½ × 3 × 4 = 6
The 3 by 10 rectangle: 3 × 10 is 30.
= the 3 by 10 rectangle: 3 × 10 = 30
The 4 by 10 rectangle: 4 × 10 is 40.
= the 4 by 10 rectangle: 4 × 10 = 40
The 5 by 10 rectangle: 5 × 10 is 50.
= the 5 by 10 rectangle: 5 × 10 = 50
Careful!
Count every face in the net.
There are two triangles, one at each end.
Careful: not 6 + 30 + 40 + 50 = 126 ✗
3 Add them all
We add all 5 faces: 132.
= SA = 6 + 6 + 30 + 40 + 50 = 132
4 Check
Let's check another way.
The three rectangles make one long strip: 12 by 10, that is 120.
Plus the two triangles, 12.
Together 132.
So the answer is right!
(3 + 4 + 5) × 10 + 2 × 6 = 120 + 12 = 132
Let's look back.
First: unfold it.
Then: area of each face.
Then: add them all.
Last: check.
Answer = SA = 6 + 6 + 30 + 40 + 50 = 132
▶ Watch it solved
The question
Question: draw the net of a triangular prism, sides 5, 12, 13, length 8, and find its surface area.
triangular prism, sides 5, 12, 13, length 8
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
Flat: three rectangles in a row, and a triangle at each end.
2 Area of each face
The two triangles: half × 5 × 12 is 30.
= the two triangles: ½ × 5 × 12 = 30
The 5 by 8 rectangle: 5 × 8 is 40.
= the 5 by 8 rectangle: 5 × 8 = 40
The 12 by 8 rectangle: 12 × 8 is 96.
= the 12 by 8 rectangle: 12 × 8 = 96
The 13 by 8 rectangle: 13 × 8 is 104.
= the 13 by 8 rectangle: 13 × 8 = 104
Careful!
Count every face in the net.
There are two triangles, one at each end.
Careful: not 30 + 40 + 96 + 104 = 270 ✗
3 Add them all
We add all 5 faces: 300.
= SA = 30 + 30 + 40 + 96 + 104 = 300
4 Check
Let's check another way.
The three rectangles make one long strip: 30 by 8, that is 240.
Plus the two triangles, 60.
Together 300.
So the answer is right!
(5 + 12 + 13) × 8 + 2 × 30 = 240 + 60 = 300
Let's look back.
First: unfold it.
Then: area of each face.
Then: add them all.
Last: check.
Answer = SA = 30 + 30 + 40 + 96 + 104 = 300
▶ Watch it solved
