Lesson 11
Polygons
Problem 1
Select all the polygons.
![Six figures labeled A, B, C, D, E, F.](https://cms-im.s3.amazonaws.com/zwbWtpTZeaa4mFmd8mjcGr1v?response-content-disposition=inline%3B%20filename%3D%226-6.1.D.PP_Image_1.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.D.PP_Image_1.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=20240727T041246Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=12a9d9da0e6ec4290f5f331243cc190cd3c1b1d9b9255e6f0a15baec5fb08506)
A
B
C
D
E
F
Solution
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Problem 2
Mark each vertex with a large dot. How many edges and vertices does this polygon have?
![12 sided polygon resembling a star](https://cms-im.s3.amazonaws.com/LD3y7y9YwqxkdKrPQXJWQXff?response-content-disposition=inline%3B%20filename%3D%226-6.1.D.PP_Image_2.1.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.D.PP_Image_2.1.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=20240727T041246Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=6798fedbc612c02c13b4067e154d6627b4a713a5fa43b665646f5548a6f336f5)
Solution
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Problem 3
Find the area of this trapezoid. Explain or show your strategy.
![Trapezoid, bases 8 and 4 units. Height 3 units.](https://cms-im.s3.amazonaws.com/avt3EEccdUpiJ2xz7Gduju2X?response-content-disposition=inline%3B%20filename%3D%226-6.1.D.PP_Image_4.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.D.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=20240727T041246Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=3f138eed4c0254658ebf17e3a2b4fd4a2f2a497ce12d2a5ad3dc6b7ef2249ae4)
Solution
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Problem 4
Lin and Andre used different methods to find the area of a regular hexagon with 6-inch sides. Lin decomposed the hexagon into six identical, equilateral triangles. Andre decomposed the hexagon into a rectangle and two triangles.
![2 identical hexagons labeled Lin’s method and Andre’s method.](https://cms-im.s3.amazonaws.com/zS6MDGFZ6zDKUinTZDYPAZFE?response-content-disposition=inline%3B%20filename%3D%226-6.1.C.PP.New.Image.17-18.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.C.PP.New.Image.17-18.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=20240727T041246Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=75a7d1681f9bc429473a414b34169cd18369fa35a82b9a3919c5bd828f01203d)
Find the area of the hexagon using each person’s method. Show your reasoning.
Solution
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Problem 5
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Identify a base and a corresponding height that can be used to find the area of this triangle. Label the base \(b\) and the corresponding height \(h\).
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Find the area of the triangle. Show your reasoning.
Solution
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(From Unit 1, Lesson 9.)Problem 6
On the grid, draw three different triangles with an area of 8 square units. Label the base and height of each triangle.
![A blank coordinate plane with 16 evenly spaced horizontal units and 12 evenly spaced vertical units.](https://cms-im.s3.amazonaws.com/Mtje8WXsjQDE9fQ8VtAvNX1D?response-content-disposition=inline%3B%20filename%3D%226-6.7.C.PP.Image.00.Blank-Grid.png%22%3B%20filename%2A%3DUTF-8%27%276-6.7.C.PP.Image.00.Blank-Grid.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=20240727T041246Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=4748c54f543ef3b87838646f5fa04b451786212b8b12d7c290d0d3bb8a4ccef4)
Solution
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(From Unit 1, Lesson 10.)