Base Area of a Prism?

John125

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Joined
May 23, 2005
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How do I get the base area of a right prism if the lateral area is 216 and the perimeter of all the sides of the triangle is 18, making each side 6. I think the formula is lateral area+ 2xB(Area of Base); but how do I get the Area of Base? The height is 12 Btw.
 
Hello, John125!

I'm trying to grasp the problem . . .

How do I get the base area of a right prism if the lateral area is 216
and the perimeter of all the sides of the triangle is 18, making each side 6.
I think the formula is lateral area+ 2xB(Area of Base);
but how do I get the Area of Base? The height is 12 Btw.
Let's see . . . we have a <u>triangular</u> prism.
The base in an <u>equlateral</u> triangle.

The lateral area is 216 . . . The height is 12.

Since the lateral area is: (height) x (perimeter of base)
. . . we have: (12) x (perimeter) = 216 . ---> . perimeter = 18

Since the base is an equilateral triangle, the side of the triangle is 6.

And you want the area of the equilateral triangle?
. . . . . . . . . . . . . . . . . . . . . . _
. . . . . . . . . . . . . . . . . . . . . √3
There is a formula: . A .= . --- s<sup>2</sup> . . . . . where s is the side of the triangle.
. . . . . . . . . . . . . . . . . . . . . .4
 
I'm trying to get the surface area... I know the lateral area is 216, and that you have to multiply that by 2x the Base Area (B). I actually have the answer, and it turns out to be 187.1. But in the work that I have for that answer it shows that you have to multiply 1/2x6x5.2 . To get the area of a triangle you must do 1/2bxh; so I get where the 6 is coming from. But where in the world does the 5.2 xcome from?

Here's a link to show you what I mean: http://www.1728.com/volprism.htm . Type in 3 for sides, 6 for side length, and 12 for height.
 
You changed the question from area of the triangle to the total surface area. Further you say you know the answer and it is 187.1

That is smaller than the 216 you say is the lateral area, so IT CANNOT BE CORRECT!!!!
I accuse you of adding interpetations of your own and mis-stating the problem!

Give us the entire original problem as stated.
---------------------------------------
Gene
 
Sorry, I meant to say the 'real' answer was 247.2 for the surface area, not 187.1, thats for the volume. Everything else is right.
 
That's nice to know. So do you still have a question or are you satisfied :?:
----------------
Gene
 
No, I still dont get how the area of the base was calculated. Why is is 5.2?
 
If the side is 6 then the height is 3*sqrt(3) = 5.2
The area = 1/2 the base times that = 3*5.2 = 15.6
-------------------
Gene
 
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