Lesson 15
More Nets, More Surface Area
Let’s draw nets and find the surface area of polyhedra.
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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T003722Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=ad9cbcacb91574b4e9b0138ae48b7d2129d8bb7d9f62fce55d7eb5a39c5d5314)
- 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.
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.
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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T003722Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=16a8e077e3c50f3e106b98225a38578ef0b4b44da5c00f82ce088a4f42250637)
- What is its surface area?
- How would the surface area change if the top two cubes are removed?
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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T003722Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d8fdfee8fc04d551fedcc9944fdf12d386269b69f3a50d233d48ec95bf5bd786)
![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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T003722Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=024f76a93c839108230ea827e53c8ec7635aface12b73ad56ef587b8622e88e5)
Problem 5
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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.)