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Pearson Geometry Common Core, 2011

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Pearson Geometry Common Core, 2011 View details

Chapter Test

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Exercise 4 Page 755

A net is a pattern made when the surface of a 3-D figure is laid out flat, showing each face of the figure. A solid may have different nets.

Net:

Verification of Euler's Formula for the Net: 6+14=19+1

Practice makes perfect

We will draw the corresponding net for the given polyhedron. Then, we will verify Euler's Formula for the 2-D shape.

Drawing the Net

A net is a pattern made when the surface of a 3-D figure is laid out flat showing each face of the figure. A solid may have different nets. The variables F, V, and E are used for different elements in 3-D and 2-D shapes.

Variable	In 3-D	In 2-D
F	Faces	Regions
V	Vertices	Vertices
E	Edges	Segments

Consider the given 3-D figure.

Let's draw a net for this solid.

Verifying Euler's Formula for the Net

In two dimensions, Euler's Formula states that the sum of the number of regions F and vertices V is one more than the number of segments E. The net we drew has 6 regions, 14 vertices, and 19 segments. Let's verify Euler's formula for our net!

F+V=E+1

SubstituteValues

Substitute values

6+ 14? = 19+1

Add terms

20=20 ✓