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
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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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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