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Finding: Surface Area of Triangular Prism 3
- Mr Kim
Please view:
Surface Area of Triangular Prism 1 & 2
Before you view this lesson
10 m
12 m
17 m
10 m
12 m
Find the Area of all 5 Faces of this Prism
17 m
17 m
10 m
12 m
Front Area is
17 m
10 m
12 m
Front Area is
21
17 m
10 m
12 m
Front Area is
1221
17 m
10 m
Front Area is
?1221
?
12 m
17 m
10 m ?1221
?
We have to find that length
12 m
17 m
10 m ?1221
We will call that unknown length
x
x
12 m
17 m
10 m ?1221
To find x we need to use Pythagoras theorem
x
12 m
17 m
10 m
12 m
?1221
x
17 m
10 m
12 m
?1221
x
Focus on this Triangle here
17 m
10 m
12 m
?1221
x
We need this length
17 m
10 m
12 m
?1221
x
And this length
17 m
10 m
12 m
?1221
x
Now if it’s 10 m here
17 m
10 m
12 m
?1221
x10 m
It’s 10 m there as well
17 m
10 m
12 m
?1221
x10 m
Now this length
17 m
10 m
12 m
?1221
x10 m
This length is half of…
17 m
10 m
12 m
?1221
x10 m
12 m
This whole length
17 m
10 m
12 m
?1221
x10 m
12 m
This whole length
17 m
10 m
12 m
?1221
x10 m
12 m
So 12 ÷ 2 =
17 m
10 m
12 m
?1221
x10 m
12 m
So 12 ÷ 2 = 6 m
6 m
17 m
10 m
12 m
?1221
x10 m
6 m
Now if we use Pythagoras theorem we
will get…
17 m
10 m
12 m
?1221
x10 m
6 m
x
x
Now if we use Pythagoras theorem we
will get…
17 m
10 m
12 m
?1221
x10 m
6 m
x
2x
squared
17 m
10 m
12 m
?1221
x10 m
6 m
x
2x
Equals
17 m
10 m
12 m
?1221
x
6 m
x10 m
22 10x
10²
17 m
10 m
12 m
?1221
x
6 m
x10 m
22 10x
The Hypotenuse (10 m) must be written
first
17 m
10 m
12 m
?1221
x
6 m
x10 m
22 10x
The Hypotenuse (10 m) must be written
first not 6
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
17 m
10 m
12 m
?1221
x
6 m
x10 m
22 10x10 m
This side is.
17 m
10 m
12 m
?1221
x
6 m
x10 m10 m
22 10x
So we MINUS
17 m
10 m
12 m
?1221
xx10 m10 m
6 m
6²
222 610 x
17 m
10 m
12 m
?1221
xx10 m10 m
6 m
222 610 x
so x equals…
x
17 m
10 m
12 m
?1221
xx10 m10 m
6 m
222 610 x
so x equals…
22 610 x
17 m
10 m
12 m
?1221
xx10 m10 m
6 m
222 610 x22 610 x
Putting this in the calculator gives…
17 m
10 m
12 m
?1221
xx10 m10 m
6 m
222 610 x22 610 x
8
17 m
10 m
12 m
?1221
xx10 m10 m
6 m
222 610 x22 610 x
8
17 m
10 m
12 m
xx10 m10 m
6 m
222 610 x22 610 x
8
81221
17 m
10 m 81221
10 m
6 m
12 m
22 610 x
222 610 x
8
8 m
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
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…
17 m
10 m 281221
10 m
6 m
12 m
22 610 x
222 610 x
8
8 m
So times by 2
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
17 m
10 m 281221
10 m
6 m
12 m
22 610 x
222 610 x
8
8 m
Add that on
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
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
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
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
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
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
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
17 m
10 m 281221
10 m
6 m
12 m
22 610 x
222 610 x
8
8 m
21710
Add that on
17 m
10 m 281221
10 m
6 m
12 m
22 610 x
222 610 x
8
8 m
21710
Bottom Area
17 m
10 m 281221
10 m
6 m
12 m
22 610 x
222 610 x
8
8 m
21710
Bottom Area
1712
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…
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…
