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January 28th, 2013, 10:57 AM   #1
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How do I find the base height of a Tetrahedron?

What I am trying to do is find the volume of a tetrahedron. However, I need the base height of the tetrahedron, which I have no idea how to figure out.

I know that the edges of the tetrahedron = 1 and the surface area is 4 times the square root of 3. Any help would be greatly appreciated.
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January 28th, 2013, 11:43 AM   #2
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Re: How do I find the base height of a Tetrahedron?

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Originally Posted by swm06
What I am trying to do is find the volume of a tetrahedron. However, I need the base height of the tetrahedron which I have no idea how to figure out.

I know that the edges of the tetrahedron = 1 and the surface area is 4 times the square root of 3. Any help would be greatly appreciated.
The surface area of a regular tetrahedron with edge 1 is
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January 28th, 2013, 04:09 PM   #3
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Re: How do I find the base height of a Tetrahedron?

Multiplied by 4 because a tetrahedron has 4 sides. But how do you find its base height?
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January 28th, 2013, 05:08 PM   #4
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Re: How do I find the base height of a Tetrahedron?

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Multiplied by 4 because a tetrahedron has 4 sides. But how do you find its base height?
The area of an equilateral triangle with side s is given by



Since the edge of the tetrahedron is s = 1, then the area of one face is



There are four faces so multiplying by 4 gives the total surface area equal to .


By the way, the height is
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January 29th, 2013, 01:44 AM   #5
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Each face of the tetrahedron has inradius of and altitude of length .

Hence the height of the tetrahedron is .
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