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Pearson Geometry Common Core, 2011

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Pearson Geometry Common Core, 2011 View details

1. Space Figures and Cross Sections

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Exercise 11 Page 692

Euler's Formula states that the sum of the number of faces and vertices of a polyhedron is two more than the number of its edges.

12

Practice makes perfect

Euler's Formula states that the sum of the number of faces F and vertices V of a polyhedron is two more than the number of its edges, E. F+ V= E+2 We are given that a polyhedron has 20 faces and 30 edges, and want to find the number of vertices. To do so, we will use Euler's formula. Let x be the number of vertices. We will substitute the given information into the formula and solve for x.

F+V=E+2

SubstituteValues

Substitute values

20+ x= 30+2

Add terms

20+x=32

LHS-20=RHS-20

x=12

We found that the polyhedron has 12 vertices.

Subchapter links

Lesson Check p.691

Practice and Problem-Solving Exercises p.692-694

Standardized Test Prep p.695

Mixed Review p.695