Lesson 14

Nets and Surface Area

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Problem 1

Can this net be assembled into a cube? Explain how you know. Label parts of the net with letters or numbers if it helps your explanation.

Net of cube 

 

Solution

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Problem 2

  1. What polyhedron can be assembled from this net? Explain how you know.

    net on a grid. 

  2. Find the surface area of this polyhedron. Show your reasoning.

Solution

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Problem 3

Here are two nets. Mai said that both nets can be assembled into the same triangular prism. Do you agree? Explain or show your reasoning.

2 nets labeled A and B. A is composed of 2 triangular and 3 rectangular faces. B is composed of the same faces, but they are arranged differently.

 

Solution

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Problem 4

Here are two three-dimensional figures.

Tell whether each of the following statements describes Figure A, Figure B, both, or neither.

Figure A triangular prism. Figure B triangular pyramid.
  1. This figure is a polyhedron.
  2. This figure has triangular faces.
  3. There are more vertices than edges in this figure.
  4. This figure has rectangular faces.
  5. This figure is a pyramid.
  6. There is exactly one face that can be the base for this figure.
  7. The base of this figure is a triangle.
  8. This figure has two identical and parallel faces that can be the base.

Solution

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(From Unit 1, Lesson 13.)

Problem 5

Select all units that can be used for surface area. 

A:

square meters

B:

feet

C:

centimeters

D:

cubic inches

E:

square inches

F:

square feet

Solution

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(From Unit 1, Lesson 12.)

Problem 6

Find the area of this polygon. Show your reasoning.

An image of a 7-sided polygon. The bottom side of the polygon is six units long, and extends out to a total width of 10 units, and a central height of 6 units.

Solution

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(From Unit 1, Lesson 11.)