Tetrahedrons - ISEE Upper Level (grades 9-12) Quantitative Reasoning

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Question

Which is the greater quantity?

(a) The surface area of a regular tetrahedron with edges of length 1

(b) 2

Answer

A regular tetrahedron has four faces, each of which is an equilateral triangle. Therefore, its surface area, given sidelength , is

$A = 4 \cdot \frac{s^{2} \sqrt{3}}{4} = s^{2} \sqrt{3}$ .

Substitute :

$A = s^{2} \sqrt{3} =1^{2} \cdot \sqrt{3} = \sqrt{3}$

$\sqrt{3} \approx 1.7 < 2$ , so (b) is greater.

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