Step by step
The question
Question: draw the net of a triangular prism, sides 3, 4, 5, length 2, and find its surface area.
triangular prism, sides 3, 4, 5, length 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
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 2 rectangle: 3 × 2 is 6.
= the 3 by 2 rectangle: 3 × 2 = 6
The 4 by 2 rectangle: 4 × 2 is 8.
= the 4 by 2 rectangle: 4 × 2 = 8
The 5 by 2 rectangle: 5 × 2 is 10.
= the 5 by 2 rectangle: 5 × 2 = 10
Careful!
Count every face in the net.
There are two triangles, one at each end.
Careful: not 6 + 6 + 8 + 10 = 30 ✗
3 Add them all
We add all 5 faces: 36.
= SA = 6 + 6 + 6 + 8 + 10 = 36
4 Check
Let's check another way.
The three rectangles make one long strip: 12 by 2, that is 24.
Plus the two triangles, 12.
Together 36.
So the answer is right!
(3 + 4 + 5) × 2 + 2 × 6 = 24 + 12 = 36
Let's look back.
First: unfold it.
Then: area of each face.
Then: add them all.
Last: check.
Answer
= SA = 6 + 6 + 6 + 8 + 10 = 36