Advanced Geometry : How to find the length of an edge
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Example Question #41 : Advanced Geometry
In order for the height of a regular tetrahedron to be one, what should the lengths of the sides be?
The formula for the height of a regular tetrahedron is 
In this case we want h to be 1, so we need something that multiplies to 1 with 
We know that 
Therefore s should be
Example Question #42 : Advanced Geometry
The volume of a regular tetrahedron is 
The formula for the volume of a regular tetrahedron is 
In this case we know that the volume, V, is 
We can simplify this by factoring 120 as the product of 8 times 15. Since the cube root of 8 is 2, we get:
Example Question #51 : Advanced Geometry
A regular tetrahedron has surface area 1,000. Which of the following comes closest to the length of one edge?
A regular tetrahedron has six congruent edges and, as its faces, four congruent equilateral triangles. If we let 
the total surface area of the tetrahedron is therefore four times this, or
Set 
Divide by 
Take the square root of both sides:
Of the given choices, 20 comes closest.
Example Question #52 : Advanced Geometry
The above figure shows a triangular pyramid, or tetrahedron, on the three-dimensional coordinate axes. The tetrahedron has volume 1,000. Which of the following is closest to the value of 
If we take the triangle on the 
Its height is the length of the side along the 
The volume of a pyramid is equal to one third the product of its height and the area of its base, so
Setting the volume 
Multiply both sides by 6:
Take the cube root of both sides:
The closest choice is 20.
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