Step by step illustration on how to find surface area of triangular prism using Pythagoras theorem to find the lesser side involved.

1. Finding: Surface Area of
Triangular Prism 3
- Mr Kim

2. Please view:
Surface Area of Triangular Prism 1 & 2
Before you view this lesson

3. 10 m
12 m
17 m

4. 10 m
12 m
Find the Area of all 5 Faces
of this Prism
17 m

5. 17 m
10 m
12 m
Front Area is

6. 17 m
10 m
12 m
Front Area is

2
1

7. 17 m
10 m
12 m
Front Area is
12
2
1


8. 17 m
10 m
Front Area is
?12
2
1

?
12 m

9. 17 m
10 m
?12
2
1

?
We have to find
that length
12 m

10. 17 m
10 m
?12
2
1

We will call that
unknown length x
x
12 m

11. 17 m
10 m
?12
2
1

To find x we need to use
Pythagoras theorem
x
12 m

12. 17 m
10 m
12 m
?12
2
1

x

13. 17 m
10 m
12 m
?12
2
1

x
Focus on this Triangle here

14. 17 m
10 m
12 m
?12
2
1

x
We need this
length

15. 17 m
10 m
12 m
?12
2
1

x
And this length

16. 17 m
10 m
12 m
?12
2
1

x
Now if it’s 10 m
here

17. 17 m
10 m
12 m
?12
2
1

x
10 m
It’s 10 m there as
well

18. 17 m
10 m
12 m
?12
2
1

x
10 m
Now this length

19. 17 m
10 m
12 m
?12
2
1

x
10 m
This length is half of…

20. 17 m
10 m
12 m
?12
2
1

x
10 m
12 m
This whole length

21. 17 m
10 m
12 m
?12
2
1

x
10 m
12 m
This whole length

22. 17 m
10 m
12 m
?12
2
1

x
10 m
12 m
So 12 ÷ 2 =

23. 17 m
10 m
12 m
?12
2
1

x
10 m
12 m
So 12 ÷ 2 = 6 m
6 m

24. 17 m
10 m
12 m
?12
2
1

x
10 m
6 m
Now if we use Pythagoras
theorem we will get…

25. 17 m
10 m
12 m
?12
2
1

x
10 m
6 m
x
x
Now if we use Pythagoras
theorem we will get…

26. 17 m
10 m
12 m
?12
2
1

x
10 m
6 m
x
2
x
squared

27. 17 m
10 m
12 m
?12
2
1

x
10 m
6 m
x
2
x
Equals

28. 17 m
10 m
12 m
?12
2
1

x
6 m
x
10 m
22
10x
10²

29. 17 m
10 m
12 m
?12
2
1

x
6 m
x
10 m
22
10x
The Hypotenuse
(10 m) must be written first

30. 17 m
10 m
12 m
?12
2
1

x
6 m
x
10 m
22
10x
The Hypotenuse
(10 m) must be written first
not 6

31. 17 m
10 m
12 m
?12
2
1

x
6 m
x
10 m
22
10x
10 m
Now x is not the longest
side of the triangle

32. 17 m
10 m
12 m
?12
2
1

x
6 m
x
10 m
22
10x
10 m
This side is.

33. 17 m
10 m
12 m
?12
2
1

x
6 m
x
10 m10 m
 22
10x
So we MINUS

34. 17 m
10 m
12 m
?12
2
1

xx
10 m10 m
6 m
6²
222
610 x

35. 17 m
10 m
12 m
?12
2
1

xx
10 m10 m
6 m
222
610 x
so x equals…
x

36. 17 m
10 m
12 m
?12
2
1

xx
10 m10 m
6 m
222
610 x
so x equals…
22
610 x

37. 17 m
10 m
12 m
?12
2
1

xx
10 m10 m
6 m
222
610 x
22
610 x
Putting this in the
calculator gives…

38. 17 m
10 m
12 m
?12
2
1

xx
10 m10 m
6 m
222
610 x
22
610 x
8

39. 17 m
10 m
12 m
?12
2
1

xx
10 m10 m
6 m
222
610 x
22
610 x
8

40. 17 m
10 m
12 m
xx
10 m10 m
6 m
222
610 x
22
610 x
8
812
2
1


41. 17 m
10 m
812
2
1

10 m
6 m
12 m
22
610 x
222
610 x
8
8 m

42. 17 m
10 m
812
2
1

10 m
6 m
12 m
22
610 x
222
610 x
8
8 m
So this is the area of
the Front face

43. 17 m
10 m
812
2
1

10 m
6 m
12 m
22
610 x
222
610 x
8
8 m
Now the Back is the
same as the Front…

44. 17 m
10 m
2812
2
1

10 m
6 m
12 m
22
610 x
222
610 x
8
8 m
So times by 2

45. 17 m
10 m
2812
2
1

10 m
6 m
12 m
22
610 x
222
610 x
8
8 m
Now find the area of
the Right Side

46. 17 m
10 m
 2812
2
1
10 m
6 m
12 m
22
610 x
222
610 x
8
8 m
Add that on

47. 17 m
10 m
 2812
2
1
10 m
6 m
12 m
22
610 x
222
610 x
8
8 m
The Right Side is a
Rectangle

48. 17 m
10 m
 2812
2
1
10 m
6 m
12 m
22
610 x
222
610 x
8
8 m
The Right Side is a
Rectangle

49. 17 m
10 m
 2812
2
1
10 m
6 m
12 m
22
610 x
222
610 x
8
8 m
The Right Side is a
Rectangle
1710

50. 17 m
10 m
 2812
2
1
10 m
6 m
12 m
22
610 x
222
610 x
8
8 m
1710
Now find the area of
the Left Side

51. 17 m
10 m
 2812
2
1
10 m
6 m
12 m
22
610 x
222
610 x
8
8 m
1710
The Left Side is the
same as the Right Side

52. 17 m
10 m
 2812
2
1
10 m
6 m
12 m
22
610 x
222
610 x
8
8 m
21710 
So times by 2

53. 17 m
10 m
 2812
2
1
10 m
6 m
12 m
22
610 x
222
610 x
8
8 m
21710 
And finally find the
Bottom Area

54. 17 m
10 m
 2812
2
1
10 m
6 m
12 m
22
610 x
222
610 x
8
8 m
 21710
Add that on

55. 17 m
10 m
 2812
2
1
10 m
6 m
12 m
22
610 x
222
610 x
8
8 m
 21710
Bottom Area

56. 17 m
10 m
 2812
2
1
10 m
6 m
12 m
22
610 x
222
610 x
8
8 m
 21710
Bottom Area
1712

57. 17 m
10 m
 2812
2
1
10 m
6 m
12 m
22
610 x
222
610 x
8
8 m
 21710
1712
Putting this altogether in
the calculator gives…

58. 17 m
10 m
 2812
2
1
10 m
6 m
12 m
22
610 x
222
610 x
8
8 m
 21710
1712
2
640m
Our Final Answer!
Putting this altogether in
the calculator gives…