Step by step
The question
Question: find the surface area of a triangular prism with triangle sides 3 m, 4 m and 5 m, and length 2 m.
1 Count the faces
The surface area is the area of all the outside faces.
This prism has 5 faces: 2 triangles and 3 rectangles.
2 The two triangles
Is there a right angle?
3 squared plus 4 squared is 9 plus 16, which is 25.
That is 5 squared.
So yes: the triangle has a right angle.
So its two short sides are its base and height: 4 m and 3 m.
One triangle is half of base times height: ½ × 4 × 3.
4 times 3 is 12.
Half of 12 means 12 divided by 2.
That is 6.
So one triangle is 6 m².
The back is the same.
Two triangles: 2 times 6 is 12.
3 The three rectangles
The bottom rectangle is 4 by 2.
This one is 5 by 2.
And this one is 3 by 2.
Unroll the three rectangles side by side.
They make one long rectangle: 4 + 5 + 3 wide and 2 long.
So the rectangles are around the triangle, times the length.
4 plus 5 plus 3 is 12.
12 times 2 is 24.
So the rectangles are 24 m².
4 Add all the faces
Add the triangles and the rectangles: 12 + 24.
12 plus 24 is 36.
So the surface area is 36 m².
Let's look back.
First: count the faces.
Then: the two triangles.
Then: the three rectangles.
Last: add all the faces.