ISEE Upper Level Math : How to find the length of an edge of a tetrahedron

Study concepts, example questions & explanations for ISEE Upper Level Math

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Example Questions

Example Question #1 : How To Find The Length Of An Edge Of A Tetrahedron

A triangular pyramid, or tetrahedron, with volume 100 has four vertices with Cartesian coordinates 

where .

Evaluate

Possible Answers:

Correct answer:

Explanation:

The tetrahedron is as follows (figure not to scale):

Tetrahedron

This is a triangular pyramid with a right triangle with legs 10 and  as its base; the area of the base is 

 

The height of the pyramid is 5, so

Set this equal to 100 to get :

 

Example Question #2 : How To Find The Length Of An Edge Of A Tetrahedron

A triangular pyramid, or tetrahedron, with volume 1,000 has four vertices with Cartesian coordinates 

where .

Evaluate 

Possible Answers:

Correct answer:

Explanation:

The tetrahedron is as follows:

Pyramid

This is a triangular pyramid with a right triangle with two legs of measure  as its base; the area of the base is 

 

Since the height of the pyramid is also , the volume is

.

Set this equal to 1,000:

Example Question #3 : How To Find The Length Of An Edge Of A Tetrahedron

A triangular pyramid, or tetrahedron, with volume 240 has four vertices with Cartesian coordinates 

where .

Evaluate 

Possible Answers:

Correct answer:

Explanation:

The tetrahedron is as follows (figure not to scale):

Tetrahedron

This is a triangular pyramid with a right triangle with two legs of measure  as its base; the area of the base is 

 

The height of the pyramid is 24, so the volume is

Set this equal to 240 to get :

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