Question 540782: A prism with a triangular base with the edges of lengths 6,8, and 10 cm has a volume of 360cubic centimeters, what is the height?! Please help... I know that V=.5Ah but dont know how to answer it! Thank you :)
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! I do not quite like your V=0.5Ah formula, but that's not your biggest problem.
Your biggest problem is that you need to find the area of that triangular base.
At first sight it looks like it will involve some complex calculations.
However, I'm guessing that you are not deemed ready for those yet, because it is a very special triangle. If you try Pythagoras theorem's formula you realize that it is a right triangle. Better yet, if you know that (3,4,5) is the most popular Pythagorean triple, you realize that your triangle is similar to a triangle with sides measuring 3, 4, and 5. It is just a scaled up version. So the 10 cm side is the hypotenuse and the other two sides, being perpendicular, can be considered base and height of that triangle.
The area of a triangle is one half the product of base times height. In this case, it would be (in square centimeters) A=(1/2)6*8=24
The volume of a prism is calculated by multiplying the area of the base by the height. (For a pyramid, it would be 1/3 of the product, but no fractional facors are needed for prisms or solids).
So for the prism, the volume (in cubic cm) is V=24h.
24h=360 --> h=360/24=15
The height of your prism is 15 cm.
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