Lesson 12
More Nets, More Surface Area
Problem 1
Jada drew a net for a polyhedron and calculated its surface area.
![Triangular prism, dimensions and areas of faces provided.](https://cms-im.s3.amazonaws.com/aTqZDMUAzxd1eDL4TR7ZKjRQ?response-content-disposition=inline%3B%20filename%3D%226-6.1.E.PP_Image_23.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.E.PP_Image_23.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T234440Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=67afb6b96b9328cf3d484aa607e9407a965c91f8c548429600254634689a08f7)
- What polyhedron can be assembled from this net?
- Jada made some mistakes in her area calculation. What were the mistakes?
- Find the surface area of the polyhedron. Show your reasoning.
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 2
A cereal box is 8 inches by 2 inches by 12 inches. What is its surface area? Show your reasoning. If you get stuck, consider drawing a sketch of the box or its net and labeling the edges with their measurements.
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 3
Twelve cubes are stacked to make this figure.
![Steps, bottom row 3 cubes, middle row 2 cubes, top row 1 cube](https://cms-im.s3.amazonaws.com/YLsysrkLAdrxDKCJ8cJoJCmW?response-content-disposition=inline%3B%20filename%3D%226-6.1.E.PP.New.Image.02.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.E.PP.New.Image.02.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T234440Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=326853554093d5634e5ad5d4688edb40b261e5474501902e2bba0e500df1172b)
- What is its surface area?
- How would the surface area change if the top two cubes are removed?
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
(From Unit 1, Lesson 10.)Problem 4
Here are two polyhedra and their nets. Label all edges in the net with the correct lengths.
![Two polyhedra labeled A and B. Polyhedron A has sides labeled 5, 4, and 10. Polyhedron B has sides labeled 4, 10, 13, 13, and 13.](https://cms-im.s3.amazonaws.com/2Xfnskoyz3sRGdqASHzMTgCW?response-content-disposition=inline%3B%20filename%3D%226-6.1.E.PP_Image_8a.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.E.PP_Image_8a.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T234440Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=73a80c0d7804930fa46c9d402519bc504abbcdeaa0e3013d351353b4dcec3cd1)
![Figure A net of rectangular prism. Figure B rectangular pyramid.](https://cms-im.s3.amazonaws.com/a2CJ1dZxE926NEUemxsATXTZ?response-content-disposition=inline%3B%20filename%3D%226-6.1.E.PP_Image_9a.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.E.PP_Image_9a.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T234440Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=be1be083453af8b826c0819ae6d36eeeea940a39c0b31790f916738dbafef097)
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 5
-
What three-dimensional figure can be assembled from the net?
- What is the surface area of the figure? (One grid square is 1 square unit.)
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
(From Unit 1, Lesson 11.)