surface area of triangular prism 2
TRANSCRIPT
![Page 1: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/1.jpg)
Finding: Surface Area of Triangular Prism 2
- Mr Kim
![Page 2: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/2.jpg)
Please view:
Surface Area of Triangular Prism 1
Before you view this lesson
![Page 3: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/3.jpg)
12 m
15 m
9.4 m
![Page 4: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/4.jpg)
12 m
15 m
9.4 m
Find the Area of all 5 Faces of this Prism
![Page 5: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/5.jpg)
12 m
15 m
9.4 m
Front Area is
![Page 6: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/6.jpg)
12 m
15 m
9.4 m
Front Area is
21
![Page 7: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/7.jpg)
12 m
15 m
9.4 m
Front Area is
121521
![Page 8: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/8.jpg)
12 m
15 m
9.4 m
Since the Back is the same as the
Front…
121521
![Page 9: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/9.jpg)
12 m
15 m
9.4 m
2121521
Times by 2
![Page 10: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/10.jpg)
12 m
15 m
9.4 m
2121521
Now let’s find the Left Side
![Page 11: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/11.jpg)
12 m
15 m
9.4 m
2121521
Add that on
![Page 12: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/12.jpg)
12 m
15 m
9.4 m
2121521
The Left side is a Rectangle
![Page 13: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/13.jpg)
12 m
15 m
9.4 m
We have…
2121521
![Page 14: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/14.jpg)
12 m
15 m
9.4 m
2121521
We have…
![Page 15: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/15.jpg)
12 m
15 m
9.4 m
2121521
But not
![Page 16: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/16.jpg)
12 m
15 m
9.4 m
2121521
We have to find that length
![Page 17: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/17.jpg)
12 m
15 m
9.4 m
2121521
We will call that unknown length
x
x
![Page 18: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/18.jpg)
12 m
15 m
9.4 m
x
To find x we need to use Pythagoras theorem
using the Front Triangle
2121521
![Page 19: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/19.jpg)
12 m
15 m
9.4 m
x
To find x we need to use Pythagoras theorem
using the Front Triangle
2121521
![Page 20: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/20.jpg)
12 m
15 m
9.4 m
x 2121521
![Page 21: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/21.jpg)
12 m
15 m
9.4 m
x
So if we use Pythagoras theorem we will get…
2121521
![Page 22: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/22.jpg)
12 m
15 m
9.4 m
x
So if we use Pythagoras theorem we will get…
x
2121521
![Page 23: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/23.jpg)
12 m
15 m
9.4 m
x
2x
squared
2121521
![Page 24: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/24.jpg)
12 m
15 m
9.4 m
x
2x
Equals
2121521
![Page 25: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/25.jpg)
12 m
15 m
9.4 m
x
152 x
Equals
2121521
![Page 26: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/26.jpg)
12 m
15 m
9.4 m
x
22 15x
squared
2121521
![Page 27: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/27.jpg)
12 m
15 m
9.4 m
x
Now, see how x is the longest side of the
triangle so we…
22 15x
2121521
![Page 28: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/28.jpg)
12 m
15 m
9.4 m
x
22 15x
Now, see how x is the longest side of the
triangle so we PLUS
2121521
![Page 29: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/29.jpg)
15 m
9.4 m
x
121522 x
12 m
2121521
12
![Page 30: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/30.jpg)
15 m
9.4 m
x
222 1215 x
squared
12 m
2121521
![Page 31: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/31.jpg)
12 m
15 m
9.4 m
x
222 1215 x
so x equals…x
2121521
![Page 32: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/32.jpg)
12 m
15 m
9.4 m
x
222 1215 xxsquare root…
2121521
![Page 33: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/33.jpg)
12 m
15 m
9.4 m
x
222 1215 xxof the whole thing
2121521
![Page 34: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/34.jpg)
12 m
15 m
9.4 m
x
222 1215 x22 1215 xof the whole thing
2121521
![Page 35: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/35.jpg)
12 m
15 m
9.4 m
x
222 1215 xBecause the opposite
of squared…
22 1215 x
2121521
![Page 36: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/36.jpg)
12 m
15 m
9.4 m
x
222 1215 x22 1215 xis square root
2121521
![Page 37: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/37.jpg)
12 m
15 m
9.4 m
x
222 1215 xPutting this in the calculator gives…
22 1215 x
2121521
![Page 38: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/38.jpg)
12 m
15 m
9.4 m
x
222 1215 xPutting this in the calculator gives…
22 1215 x2.19x
2121521
![Page 39: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/39.jpg)
12 m
15 m
9.4 m
222 1215 xSo the unknown length is 19.2 m
22 1215 x2.19x
2121521 19.2
m
![Page 40: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/40.jpg)
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
Now let’s find the Area of the Left
Side
2121521
![Page 41: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/41.jpg)
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
Now let’s find the Area of the Left
Side
2121521
![Page 42: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/42.jpg)
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
2.194.9
2121521
Now let’s find the Area of the Left
Side
![Page 43: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/43.jpg)
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
2.194.9
Now find the Area of the Right Side
2121521
![Page 44: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/44.jpg)
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
2.194.9
2121521
Add that on
![Page 45: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/45.jpg)
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
So the Area of the Right Side is
2.194.9
2121521
![Page 46: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/46.jpg)
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
12
2.194.9
2121521
So the Area of the Right Side is
![Page 47: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/47.jpg)
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
So the Area of the Right Side is
12
2.194.9
2121521
![Page 48: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/48.jpg)
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
If it’s 9.4 m there
12
2.194.9
2121521
![Page 49: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/49.jpg)
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
12
9.4 m 2.194.9
2121521
It’s 9.4 m there as well
![Page 50: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/50.jpg)
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
4.912
9.4 m 2.194.9
2121521
It’s 9.4 m there as well
![Page 51: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/51.jpg)
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
4.912
9.4 m
And finally, find the Bottom Area
2.194.9
2121521
![Page 52: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/52.jpg)
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
4.912
9.4 m 2.194.9
2121521
Add that on
![Page 53: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/53.jpg)
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
9.4 m
Bottom Area
4.912 2.194.9
2121521
![Page 54: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/54.jpg)
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
9.4 m
154.9
4.912 2.194.9
2121521
Bottom Area
![Page 55: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/55.jpg)
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
9.4 m
154.9
4.912 2.194.9
2121521
Putting this altogether in the calculator
gives…
![Page 56: Surface Area of Triangular Prism 2](https://reader033.vdocuments.net/reader033/viewer/2022061508/58a0a1041a28ab9f758b63c7/html5/thumbnails/56.jpg)
12 m
15 m
9.4 m
19.2 m
222 1215 x22 1215 x
2.19x
9.4 m
23.614154.9 m
4.912 2.194.9
2121521
Putting this altogether in the calculator
gives…
Our Final Answer!