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What is the area of the polygon below?

What is the area of the polygon below?

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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**Title: Calculating the Area of an Irregular Polygon** **Question:** What is the area of the polygon below? **Description:** The image provided shows an irregular polygon drawn on a coordinate plane. The coordinate plane is represented by a grid of squares, each square being a unit by unit of measurements. The polygon is enclosed by a solid black line and its interior is shaded lightly for distinction. **Instructions:** 1. **Analyzing the Grid**: To determine the area of the polygon, it is useful to utilize the grid provided. Each square on the grid represents a unit area. By estimating or calculating the number of full and partial squares covered by the polygon, we can determine its total area. 2. **Counting Full Squares**: Count the number of complete squares within the shaded area. Each complete square contributes an area of 1 square unit. 3. **Estimating Partial Squares**: For partial squares, you can estimate their combined areas. For simplicity, you may break these into approximate halves and quarters, then sum them up. 4. **Summing Up Areas**: - Add up the areas of all full squares. - Add up the areas of all fractions of squares. 5. **Final Calculation**: The total area of the polygon is the sum of the areas of full and partial squares. This exercise helps in understanding practical methods of determining the area of irregular shapes using grid approximation. It enhances spatial understanding and provides a clear visual representation of area calculation techniques.
Transcribed Image Text:**Title: Calculating the Area of an Irregular Polygon** **Question:** What is the area of the polygon below? **Description:** The image provided shows an irregular polygon drawn on a coordinate plane. The coordinate plane is represented by a grid of squares, each square being a unit by unit of measurements. The polygon is enclosed by a solid black line and its interior is shaded lightly for distinction. **Instructions:** 1. **Analyzing the Grid**: To determine the area of the polygon, it is useful to utilize the grid provided. Each square on the grid represents a unit area. By estimating or calculating the number of full and partial squares covered by the polygon, we can determine its total area. 2. **Counting Full Squares**: Count the number of complete squares within the shaded area. Each complete square contributes an area of 1 square unit. 3. **Estimating Partial Squares**: For partial squares, you can estimate their combined areas. For simplicity, you may break these into approximate halves and quarters, then sum them up. 4. **Summing Up Areas**: - Add up the areas of all full squares. - Add up the areas of all fractions of squares. 5. **Final Calculation**: The total area of the polygon is the sum of the areas of full and partial squares. This exercise helps in understanding practical methods of determining the area of irregular shapes using grid approximation. It enhances spatial understanding and provides a clear visual representation of area calculation techniques.
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