Step by step
The question
Question: find the surface area of a triangular prism with triangle base 8 cm, height 3 cm and sides 5 cm, and length 7 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
The triangle has base 8 cm and height 3 cm.
One triangle is half of base times height: ½ × 8 × 3.
8 times 3 is 24.
Half of 24 means 24 divided by 2.
That is 12.
So one triangle is 12 cm².
The back is the same.
Two triangles: 2 times 12 is 24.
3 The three rectangles
The bottom rectangle is 8 by 7.
This one is 5 by 7.
And this one is 5 by 7.
Unroll the three rectangles side by side.
They make one long rectangle: 8 + 5 + 5 wide and 7 long.
So the rectangles are around the triangle, times the length.
8 plus 5 plus 5 is 18.
18 times 7 is 126.
So the rectangles are 126 cm².
4 Add all the faces
Add the triangles and the rectangles: 24 + 126.
24 plus 126 is 150.
So the surface area is 150 cm².
Let's look back.
First: count the faces.
Then: the two triangles.
Then: the three rectangles.
Last: add all the faces.