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Explain why it would be confusing to say that the darkly shaded squares in the figure represent the 0.5-unit and 0.8-unit lengths you use in the length x width formula for the area of the shaded rectangle. -1 unit-

Explain why it would be confusing to say that the darkly shaded squares in the figure represent the 0.5-unit and 0.8-unit lengths you use in the length x width formula for the area of the shaded rectangle. -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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**Understanding Length Units in Area Calculations** In this section, we will clear up potential confusion that can arise when interpreting shaded areas on a grid, particularly when determining the area of a rectangle using the formula **length x width**. ### Visual Aid: Shaded Rectangle on a Grid #### Description of the Diagram The diagram presents a grid with 11 columns and 8 rows of smaller squares. Two sections of the grid are shaded in different shades: - **Darkly Shaded Squares**: These are four squares on the top row of the grid. Each darkly shaded square is aligned horizontally. - **Lightly Shaded Squares**: These are the remaining squares in a rectangular block connected to the darkly shaded squares. There are total of 8 lightly shaded squares arranged in a 2 x 4 block (two rows and four columns). #### Detailed Analysis of Units The total width of the shaded region, including both the darkly shaded and lightly shaded squares, is labeled as **1 unit**: - Each individual square within the grid represents a certain fraction of this 1-unit length. ### Why Clarity is Crucial Now, let's focus on the question: why would it be **confusing** to say the darkly shaded squares correspond to 0.5-unit and 0.8-unit lengths? Here are the key points: 1. **Inconsistent Fractional Representation**: - Assigning 0.5-unit or 0.8-unit lengths to the darkly shaded squares would imply that each of these squares represents a fractional part of 1 unit, which might not align uniformly with the grid system. 2. **Uniform Square Dimensions**: - Each square in the grid appears to have equal dimensions. Therefore, it is critical to interpret these squares consistently in relation to one another when calculating area. 3. **Calculation Consistency**: - For accurate calculation of the area using the **length x width** formula, we must comprehend that the entire shaded area collectively measures to a whole unit (or another identifiable uniform measure), thus maintaining consistency across calculations. ### Conclusion By ensuring a clear and consistent interpretation of the grid units, learners can accurately apply the **length x width** formula for determining the area of the shaded rectangle. This understanding prevents errors and ensures clarity in mathematical reasoning.
Transcribed Image Text:**Understanding Length Units in Area Calculations** In this section, we will clear up potential confusion that can arise when interpreting shaded areas on a grid, particularly when determining the area of a rectangle using the formula **length x width**. ### Visual Aid: Shaded Rectangle on a Grid #### Description of the Diagram The diagram presents a grid with 11 columns and 8 rows of smaller squares. Two sections of the grid are shaded in different shades: - **Darkly Shaded Squares**: These are four squares on the top row of the grid. Each darkly shaded square is aligned horizontally. - **Lightly Shaded Squares**: These are the remaining squares in a rectangular block connected to the darkly shaded squares. There are total of 8 lightly shaded squares arranged in a 2 x 4 block (two rows and four columns). #### Detailed Analysis of Units The total width of the shaded region, including both the darkly shaded and lightly shaded squares, is labeled as **1 unit**: - Each individual square within the grid represents a certain fraction of this 1-unit length. ### Why Clarity is Crucial Now, let's focus on the question: why would it be **confusing** to say the darkly shaded squares correspond to 0.5-unit and 0.8-unit lengths? Here are the key points: 1. **Inconsistent Fractional Representation**: - Assigning 0.5-unit or 0.8-unit lengths to the darkly shaded squares would imply that each of these squares represents a fractional part of 1 unit, which might not align uniformly with the grid system. 2. **Uniform Square Dimensions**: - Each square in the grid appears to have equal dimensions. Therefore, it is critical to interpret these squares consistently in relation to one another when calculating area. 3. **Calculation Consistency**: - For accurate calculation of the area using the **length x width** formula, we must comprehend that the entire shaded area collectively measures to a whole unit (or another identifiable uniform measure), thus maintaining consistency across calculations. ### Conclusion By ensuring a clear and consistent interpretation of the grid units, learners can accurately apply the **length x width** formula for determining the area of the shaded rectangle. This understanding prevents errors and ensures clarity in mathematical reasoning.
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