GMAT Math : Tetrahedrons

Study concepts, example questions & explanations for GMAT Math

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Example Questions

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Example Question #9 : Calculating The Surface Area Of A Tetrahedron

Tetra_1

The cube in the above figure has surface area 384. Give the surface area of the tetrahedron with vertices , shown in red.

Possible Answers:

Correct answer:

Explanation:

The surface area formula can be used to find the length of each edge of the cube:

Three faces of the tetrahedron - ,   - are right triangles with legs of length 8, so the area of each is half the product of the lengths of their legs:

.

Each triangle is isosceles, so, by the 45-45-90 Theorem, each of their hypotentuses measures  times a leg, or .  is therefore an equilateral triangle with sidelenghth . Its area can be found as follows:

The total surface area is 

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