Download - Surface Area of Triangular Prism 3
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Finding: Surface Area of Triangular Prism 3
- Mr Kim
![Page 2: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/2.jpg)
Please view:
Surface Area of Triangular Prism 1 & 2
Before you view this lesson
![Page 3: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/3.jpg)
10 m
12 m
17 m
![Page 4: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/4.jpg)
10 m
12 m
Find the Area of all 5 Faces of this Prism
17 m
![Page 5: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/5.jpg)
17 m
10 m
12 m
Front Area is
![Page 6: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/6.jpg)
17 m
10 m
12 m
Front Area is
21
![Page 7: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/7.jpg)
17 m
10 m
12 m
Front Area is
1221
![Page 8: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/8.jpg)
17 m
10 m
Front Area is
?1221
?
12 m
![Page 9: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/9.jpg)
17 m
10 m ?1221
?
We have to find that length
12 m
![Page 10: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/10.jpg)
17 m
10 m ?1221
We will call that unknown length
x
x
12 m
![Page 11: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/11.jpg)
17 m
10 m ?1221
To find x we need to use Pythagoras theorem
x
12 m
![Page 12: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/12.jpg)
17 m
10 m
12 m
?1221
x
![Page 13: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/13.jpg)
17 m
10 m
12 m
?1221
x
Focus on this Triangle here
![Page 14: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/14.jpg)
17 m
10 m
12 m
?1221
x
We need this length
![Page 15: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/15.jpg)
17 m
10 m
12 m
?1221
x
And this length
![Page 16: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/16.jpg)
17 m
10 m
12 m
?1221
x
Now if it’s 10 m here
![Page 17: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/17.jpg)
17 m
10 m
12 m
?1221
x10 m
It’s 10 m there as well
![Page 18: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/18.jpg)
17 m
10 m
12 m
?1221
x10 m
Now this length
![Page 19: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/19.jpg)
17 m
10 m
12 m
?1221
x10 m
This length is half of…
![Page 20: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/20.jpg)
17 m
10 m
12 m
?1221
x10 m
12 m
This whole length
![Page 21: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/21.jpg)
17 m
10 m
12 m
?1221
x10 m
12 m
This whole length
![Page 22: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/22.jpg)
17 m
10 m
12 m
?1221
x10 m
12 m
So 12 ÷ 2 =
![Page 23: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/23.jpg)
17 m
10 m
12 m
?1221
x10 m
12 m
So 12 ÷ 2 = 6 m
6 m
![Page 24: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/24.jpg)
17 m
10 m
12 m
?1221
x10 m
6 m
Now if we use Pythagoras theorem we
will get…
![Page 25: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/25.jpg)
17 m
10 m
12 m
?1221
x10 m
6 m
x
x
Now if we use Pythagoras theorem we
will get…
![Page 26: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/26.jpg)
17 m
10 m
12 m
?1221
x10 m
6 m
x
2x
squared
![Page 27: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/27.jpg)
17 m
10 m
12 m
?1221
x10 m
6 m
x
2x
Equals
![Page 28: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/28.jpg)
17 m
10 m
12 m
?1221
x
6 m
x10 m
22 10x
10²
![Page 29: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/29.jpg)
17 m
10 m
12 m
?1221
x
6 m
x10 m
22 10x
The Hypotenuse (10 m) must be written
first
![Page 30: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/30.jpg)
17 m
10 m
12 m
?1221
x
6 m
x10 m
22 10x
The Hypotenuse (10 m) must be written
first not 6
![Page 31: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/31.jpg)
17 m
10 m
12 m
?1221
x
6 m
x10 m
22 10x10 m
Now x is not the longest side of the triangle
![Page 32: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/32.jpg)
17 m
10 m
12 m
?1221
x
6 m
x10 m
22 10x10 m
This side is.
![Page 33: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/33.jpg)
17 m
10 m
12 m
?1221
x
6 m
x10 m10 m
22 10x
So we MINUS
![Page 34: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/34.jpg)
17 m
10 m
12 m
?1221
xx10 m10 m
6 m
6²
222 610 x
![Page 35: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/35.jpg)
17 m
10 m
12 m
?1221
xx10 m10 m
6 m
222 610 x
so x equals…
x
![Page 36: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/36.jpg)
17 m
10 m
12 m
?1221
xx10 m10 m
6 m
222 610 x
so x equals…
22 610 x
![Page 37: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/37.jpg)
17 m
10 m
12 m
?1221
xx10 m10 m
6 m
222 610 x22 610 x
Putting this in the calculator gives…
![Page 38: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/38.jpg)
17 m
10 m
12 m
?1221
xx10 m10 m
6 m
222 610 x22 610 x
8
![Page 39: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/39.jpg)
17 m
10 m
12 m
?1221
xx10 m10 m
6 m
222 610 x22 610 x
8
![Page 40: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/40.jpg)
17 m
10 m
12 m
xx10 m10 m
6 m
222 610 x22 610 x
8
81221
![Page 41: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/41.jpg)
17 m
10 m 81221
10 m
6 m
12 m
22 610 x
222 610 x
8
8 m
![Page 42: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/42.jpg)
17 m
10 m 81221
10 m
6 m
12 m
22 610 x
222 610 x
8
8 m
So this is the area of the Front face
![Page 43: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/43.jpg)
17 m
10 m 81221
10 m
6 m
12 m
22 610 x
222 610 x
8
8 m
Now the Back is the same as the Front…
![Page 44: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/44.jpg)
17 m
10 m 281221
10 m
6 m
12 m
22 610 x
222 610 x
8
8 m
So times by 2
![Page 45: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/45.jpg)
17 m
10 m 281221
10 m
6 m
12 m
22 610 x
222 610 x
8
8 m
Now find the area of the Right Side
![Page 46: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/46.jpg)
17 m
10 m 281221
10 m
6 m
12 m
22 610 x
222 610 x
8
8 m
Add that on
![Page 47: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/47.jpg)
17 m
10 m 281221
10 m
6 m
12 m
22 610 x
222 610 x
8
8 m
The Right Side is a Rectangle
![Page 48: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/48.jpg)
17 m
10 m 281221
10 m
6 m
12 m
22 610 x
222 610 x
8
8 m
The Right Side is a Rectangle
![Page 49: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/49.jpg)
17 m
10 m 281221
10 m
6 m
12 m
22 610 x
222 610 x
8
8 m
The Right Side is a Rectangle
1710
![Page 50: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/50.jpg)
17 m
10 m 281221
10 m
6 m
12 m
22 610 x
222 610 x
8
8 m
1710
Now find the area of the Left Side
![Page 51: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/51.jpg)
17 m
10 m 281221
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
![Page 52: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/52.jpg)
17 m
10 m 281221
10 m
6 m
12 m
22 610 x
222 610 x
8
8 m
21710
So times by 2
![Page 53: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/53.jpg)
17 m
10 m 281221
10 m
6 m
12 m
22 610 x
222 610 x
8
8 m
21710
And finally find the Bottom Area
![Page 54: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/54.jpg)
17 m
10 m 281221
10 m
6 m
12 m
22 610 x
222 610 x
8
8 m
21710
Add that on
![Page 55: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/55.jpg)
17 m
10 m 281221
10 m
6 m
12 m
22 610 x
222 610 x
8
8 m
21710
Bottom Area
![Page 56: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/56.jpg)
17 m
10 m 281221
10 m
6 m
12 m
22 610 x
222 610 x
8
8 m
21710
Bottom Area
1712
![Page 57: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/57.jpg)
17 m
10 m 281221
10 m
6 m
12 m
22 610 x
222 610 x
8
8 m
21710
1712
Putting this altogether in the calculator gives…
![Page 58: Surface Area of Triangular Prism 3](https://reader035.vdocument.in/reader035/viewer/2022062316/58a0a11f1a28ab9f758b6421/html5/thumbnails/58.jpg)
17 m
10 m 281221
10 m
6 m
12 m
22 610 x
222 610 x
8
8 m
21710
17122640m
Our Final Answer!
Putting this altogether in the calculator gives…