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Geometry

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by swerve » Wed Aug 19, 2020 12:05 pm
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If all the faces of pyramid P (including the base) are equilateral triangles of side 2, what is the surface area of pyramid P?

A. \(4+\dfrac{3\sqrt{3}}{4}\)
B. \(4\sqrt{3}\)
C. \(4+3\sqrt{3}\)
D. \(6\sqrt{3}\)
E. \(12\)

The OA is B


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Re: Geometry

by Scott@TargetTestPrep » Sat Aug 22, 2020 10:48 am
swerve wrote: ↑
Wed Aug 19, 2020 12:05 pm
 If all the faces of pyramid P (including the base) are equilateral triangles of side 2, what is the surface area of pyramid P?

A. \(4+\dfrac{3\sqrt{3}}{4}\)
B. \(4\sqrt{3}\)
C. \(4+3\sqrt{3}\)
D. \(6\sqrt{3}\)
E. \(12\)

The OA is B


Solution:

The pyramid has 4 triangular faces. Since each face is an equilateral triangle with side length of 2, its area is (√3 * 2^2)/4 = (√3 * 4)/4 = √3. Since the pyramid has 4 (equal-area) faces, the surface area of the pyramid is √3 * 4 = 4√3.

Answer: B

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