How to find the volume of this prism?

Question

anonymous · Answer

attachment

anonymous · Answer

Lateral Area is$$12 \sqrt{3}$$

anonymous · Answer

@saifoo.khan

saifoo.khan · Answer

Base area * height?

anonymous · Answer

i am having trouble finding the base area. is that the pythagorean theorem?

mathmale · Answer

What shape does the base seem to have?

Unfortunately, this drawing does not specifically state that the base is a RIGHT triangle, or just a triangle, or what.  

If I'm reading this problem statement correctly, we are told that the "lateral area" of this prism is 12*Sqrt(3).  Assuming that you agree with that, you might want to use this fact to determine the height of this prism.  Knowing the height is essential when we calculate the volume.

anonymous · Answer

Yes, the lateral area is definitely 12 sqrt (3). I am not sure either about whether or not the base is a right triangle, it didn't say for sure, but I am assuming that it is not a right triangle. @mathmale

mathmale · Answer

I'd suggest that you experiment.  Arbitrarily state that the base IS a right triangle, and then attempt to solve the problem based upon that.  Next, determine how you'd find the volume of the prism were the base NOT a right triangle.

If we DO arbitrarily state that the base IS a right triangle, then it is also an isosceles right triangle of side length 4 and hypotenuse 4Sqrt(2).  That hypotenuse is represented by the dotted line in the diagram. 

If the lateral area (not including the base) is 12Sqrt(3), then what is the height of the prism?