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A regular icosahedron is a three-dimensional solid composed of twenty

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by BTGModeratorVI » Fri Jul 03, 2020 7:22 am

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A regular icosahedron is a three-dimensional solid composed of twenty equilateral triangular faces, with five faces meeting at each vertex. How many vertices does a regular icosahedron have?

A. 5
B. 12
C. 20
D. 33
E. 60

Answer: B
Source: Veritas Prep
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Re: A regular icosahedron is a three-dimensional solid composed of twenty

by Brent@GMATPrepNow » Fri Jul 03, 2020 8:11 am
BTGModeratorVI wrote: ↑
Fri Jul 03, 2020 7:22 am
 A regular icosahedron is a three-dimensional solid composed of twenty equilateral triangular faces, with five faces meeting at each vertex. How many vertices does a regular icosahedron have?

A. 5
B. 12
C. 20
D. 33
E. 60

Answer: B
Source: Veritas Prep
Each triangle has 3 vertices, and there are 20 triangles in total.
So, the total number of triangle vertices = 3 x 20 = 60

Each vertex in the icosahedron is comprised of five triangle faces meeting at a point.
In other words, it takes 5 triangle vertices to make 1 icosahedron vertex .
We have 60 triangle vertices, so the TOTAL number of icosahedron vertices = 60/5 = 12

Answer: B

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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