Lesson 13
Polyhedra
Let’s investigate polyhedra.
Problem 1
Select all the polyhedra.
![Figure A rectangular pyramid. Figure B many sided polyhedron. Figure C cone. Figure D Prism with hexagon faces. Figure E sphere.](https://cms-im.s3.amazonaws.com/w5KuSmm66D7KoaNLVa24nM9C?response-content-disposition=inline%3B%20filename%3D%226-6.1.E.PP_Image_2.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.E.PP_Image_2.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=20240727T004948Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=427bb9ae9ddbb58d208dd25ecb1ad7862338369dc6910a5f5282f942176e75d6)
A:
A
B:
B
C:
C
D:
D
E:
E
Problem 2
-
Is this polyhedron a prism, a pyramid, or neither? Explain how you know.
- How many faces, edges, and vertices does it have?
Problem 3
Tyler said this net cannot be a net for a square prism because not all the faces are squares.
Do you agree with Tyler? Explain your reasoning.
![net. 4 adjacent rectangles. Square above rectangle 2 and beow rectangle 1.](https://cms-im.s3.amazonaws.com/qPD7z53XdqsNQyqVdhQ11nRp?response-content-disposition=inline%3B%20filename%3D%226-6.1.E.PP.New.Image.11.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.E.PP.New.Image.11.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=20240727T004948Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=11cd9087a8a45e8ee909172ab79fd27649969068c1874108f701667c4a3b5c9f)
Problem 4
Explain why each of these triangles has an area of 9 square units.
![Three triangles labeled A, B, and, C. Each triangle has a bas of 6 units and a height of 3 units.](https://cms-im.s3.amazonaws.com/NQepdH7puEBLUkSc2JZToGG5?response-content-disposition=inline%3B%20filename%3D%226-6.1.C.PP.New.Image.08.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.C.PP.New.Image.08.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=20240727T004948Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=a1e4998e168567a1d03569d2b013f136e249fb18d6e92ede0953e80034bcacc7)
Problem 5
-
A parallelogram has a base of 12 meters and a height of 1.5 meters. What is its area?
- A triangle has a base of 16 inches and a height of \(\frac18\) inches. What is its area?
- A parallelogram has an area of 28 square feet and a height of 4 feet. What is its base?
- A triangle has an area of 32 square millimeters and a base of 8 millimeters. What is its height?
Problem 6
Find the area of the shaded region. Show or explain your reasoning.
![Triangle shaded with a unshaded square located in the middle on the bottom.](https://cms-im.s3.amazonaws.com/J1qEMcijroqnTp77iHX5Z1ZH?response-content-disposition=inline%3B%20filename%3D%226-6.1.A.PP_Image_17.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.A.PP_Image_17.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=20240727T004948Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=278d9fde4dee4a4127c224f49c185f91c37bf2cc1da87e8371a9664d84a71c14)