Lesson 14
Nets and Surface Area
Let’s use nets to find the surface area of polyhedra.
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=20240727T002748Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e896ca4d06f8cec2d058bd89511365d3f4142dc0129b0a8cf8019a3c12698e49)
Problem 2
-
What polyhedron can be assembled from this net? Explain how you know.
- Find the surface area of this polyhedron. Show your reasoning.
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=20240727T002748Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=02c0e2daa1075f2ccd24f30effdf1edaa261e91bb05e992945e9a8eb06c61924)
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=20240727T002748Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e0db2db8aa988b4dfc1de0cdfbf1271cbd0548bccea9da5bea4d56d1463ae4fa)
- 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.
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:
(From Unit 1, Lesson 12.)
square feet
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=20240727T002748Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=ab0cec53ed56207523754d543b631f5823e7fbc2536fbd6a2188085129325870)