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Example Question #9 : Calculating The Surface Area Of A Tetrahedron
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
James
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University of Kansas, Bachelor in Arts, Art History. Yale University, Master of Arts, History of Art.
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