math question?

Question

find the volume of the triangullar prism. the area of the largest surface is 240 in^2.
http://i117.photobucket.com/albums/o57/missoua/math1.jpg

Answer 1

OK!
Firstly I should tell you that the given data in your problem are enough and you can solve it
Here is the solution:

Now that you know the data are enough, use the given area of the largest surface to find the unknown side. Since this area is a rectangle:
12 * c = 240 square inches
=> c = 20 in

Now use the two known sides of the front triangle to find the lenght of the unknown side. Use this triangle equation:

a ^ 2 + b ^ 2 = c ^ 2

16 ^ 2 + b ^ 2 = 20 ^ 2
=> b = 12 in

So the volume = {(b * a)/2} * 12 = 1152 cubic inches.

Good luck my friend!

P.S. You can use the 16/20 = cos t where t = the top angel of the front triangle to find the length bottom side of the front triangle.
Cos t = 16/20 = 0.8 => b = 36.87 degrees.
Sin t = b/20
Sin t = 0.6 => b/20 = 0.6 => b = 12

Answer 2

The largest area is the sloping face. Other faces have shorter sides.
It is a rectangle, so 12 * x = 240, giving x = 20, for the long side – hypotenuse of the (right) triangular face. Then, by Pythagoras’, the other side is 12.

So the volume is (area of triangle) * (distance between) triangles,
= (½ * 12 * 16) * 12 in^3
= 1152 in^3 .

Answer 3

In order to find the volume you would have to know a 3rd length because the area only gives you either l times width or l times height or w times height in any case we need a third lenght because volume is 1/2lwh