Step by step
The question
Question: find the surface area of a triangular prism with triangle base 10 m, height 12 m and sides 13 m, and length 3 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
The triangle has base 10 m and height 12 m.
One triangle is half of base times height: ½ × 10 × 12.
10 times 12 is 120.
Half of 120 means 120 divided by 2.
That is 60.
So one triangle is 60 m².
The back is the same.
Two triangles: 2 times 60 is 120.
3 The three rectangles
The bottom rectangle is 10 by 3.
This one is 13 by 3.
And this one is 13 by 3.
Unroll the three rectangles side by side.
They make one long rectangle: 10 + 13 + 13 wide and 3 long.
So the rectangles are around the triangle, times the length.
10 plus 13 plus 13 is 36.
36 times 3 is 108.
So the rectangles are 108 m².
4 Add all the faces
Add the triangles and the rectangles: 120 + 108.
120 plus 108 is 228.
So the surface area is 228 m².
Let's look back.
First: count the faces.
Then: the two triangles.
Then: the three rectangles.
Last: add all the faces.