Lesson 14
Nets and Surface Area
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](https://cms-im.s3.amazonaws.com/TcyrwfChUcodqgeebQ5CWMgC?response-content-disposition=inline%3B%20filename%3D%226-6.1.E.PP_Image_13.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.E.PP_Image_13.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000255Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=fcd41c7c6e9b63b4c1bbd9bbad0814773a2c30a311ccaf41db3ef3c794d3ca8b)
Solution
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Problem 2
-
What polyhedron can be assembled from this net? Explain how you know.
- 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.](https://cms-im.s3.amazonaws.com/iZiwj6jV2imycgobWmjEHot1?response-content-disposition=inline%3B%20filename%3D%226-6.1.E.PP.New.Image.15.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.E.PP.New.Image.15.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000255Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=247f3184e808df320bee24da8cf5e5c9a2064d209985fa10798d0031ff94f619)
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.](https://cms-im.s3.amazonaws.com/GMeWfd8yn4mH4Hm3EvM9TK2Y?response-content-disposition=inline%3B%20filename%3D%226-6.1.E.PP_Image_4.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.E.PP_Image_4.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000255Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=a891bffbb886bc1d3643f2bfa582f45a06591b8a51f32fa47277a5af251c65b9)
- This figure is a polyhedron.
- This figure has triangular faces.
- There are more vertices than edges in this figure.
- This figure has rectangular faces.
- This figure is a pyramid.
- There is exactly one face that can be the base for this figure.
- The base of this figure is a triangle.
- 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.
square meters
feet
centimeters
cubic inches
square inches
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.](https://cms-im.s3.amazonaws.com/wkUVdNnfsPBeyrgZdZo4PULs?response-content-disposition=inline%3B%20filename%3D%226-6.1.D.PP.New.Image.02.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.D.PP.New.Image.02.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000255Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e02b363a6d37d6a54c8e9f5839fa469cf1ef3444ee2914a86588aaa32249e31d)
Solution
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(From Unit 1, Lesson 11.)