Step by step
The question
Question: find the surface area of a triangular prism with triangle sides 6 cm, 8 cm and 10 cm, and length 5 cm.
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?
6 squared plus 8 squared is 36 plus 64, which is 100.
That is 10 squared.
So yes: the triangle has a right angle.
So its two short sides are its base and height: 8 cm and 6 cm.
One triangle is half of base times height: ½ × 8 × 6.
8 times 6 is 48.
Half of 48 means 48 divided by 2.
That is 24.
So one triangle is 24 cm².
The back is the same.
Two triangles: 2 times 24 is 48.
3 The three rectangles
The bottom rectangle is 8 by 5.
This one is 10 by 5.
And this one is 6 by 5.
Unroll the three rectangles side by side.
They make one long rectangle: 8 + 10 + 6 wide and 5 long.
So the rectangles are around the triangle, times the length.
8 plus 10 plus 6 is 24.
24 times 5 is 120.
So the rectangles are 120 cm².
4 Add all the faces
Add the triangles and the rectangles: 48 + 120.
48 plus 120 is 168.
So the surface area is 168 cm².
Let's look back.
First: count the faces.
Then: the two triangles.
Then: the three rectangles.
Last: add all the faces.