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9. Determine the area of the shaded shapes in Figure 12.55. Explain your reasoning. 1 unit ● Figure 12.55 Determining the areas of shapes. ● ● Bondi sbra 1 unit

9. Determine the area of the shaded shapes in Figure 12.55. Explain your reasoning. 1 unit ● Figure 12.55 Determining the areas of shapes. ● ● Bondi sbra 1 unit

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Explain your reasoning.

### Chapter of Parallelograms and Other Polygons #### 9. Determine the area of the shaded shapes in Figure 12.55. Explain your reasoning. **Figure 12.55: Determining the areas of shapes** **Description**: The figure consists of two separate diagrams with shaded polygons placed on a grid of dots. Each unit measurement on the grid is indicated as 1 unit. There are black lines connecting certain dots to form the geometric shapes. **First Diagram (left side)**: This diagram shows a star-shaped polygon with five points, each point comprising a triangle converging at the center. The boundaries of these triangles interact with several of the grid's dots, but the exact vertices and enclosed area will need to be analyzed to determine the total area. **Second Diagram (right side)**: This diagram illustrates a more complex, symmetrical shape that overall resembles an "M" structure but with additional triangular and trapezoidal formations. Similar to the first diagram, the vertices of the shapes lie on the dots of the grid, and calculation of the total area will use these formations. To determine the area of each shaded shape, break down the complex polygons into smaller and more manageable shapes (such as triangles, rectangles, and trapezoids), then calculate their areas based on the grid's unit measurements. Summing these smaller areas will give the total area of each shaded polygon. For accurate results, carefully identify the vertices of each small shape on the grid and use the distance between the dots (1 unit) as the basis for calculating side lengths.
Transcribed Image Text:### Chapter of Parallelograms and Other Polygons #### 9. Determine the area of the shaded shapes in Figure 12.55. Explain your reasoning. **Figure 12.55: Determining the areas of shapes** **Description**: The figure consists of two separate diagrams with shaded polygons placed on a grid of dots. Each unit measurement on the grid is indicated as 1 unit. There are black lines connecting certain dots to form the geometric shapes. **First Diagram (left side)**: This diagram shows a star-shaped polygon with five points, each point comprising a triangle converging at the center. The boundaries of these triangles interact with several of the grid's dots, but the exact vertices and enclosed area will need to be analyzed to determine the total area. **Second Diagram (right side)**: This diagram illustrates a more complex, symmetrical shape that overall resembles an "M" structure but with additional triangular and trapezoidal formations. Similar to the first diagram, the vertices of the shapes lie on the dots of the grid, and calculation of the total area will use these formations. To determine the area of each shaded shape, break down the complex polygons into smaller and more manageable shapes (such as triangles, rectangles, and trapezoids), then calculate their areas based on the grid's unit measurements. Summing these smaller areas will give the total area of each shaded polygon. For accurate results, carefully identify the vertices of each small shape on the grid and use the distance between the dots (1 unit) as the basis for calculating side lengths.
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