Goals
1. Understand how enlarging and reducing geometric figures affects their metric properties, including area and perimeter.
2. Calculate the area and perimeter for both enlarged and reduced figures.
3. Develop practical skills applicable in real-world situations such as design, architecture, and engineering.
Contextualization
Imagine you’re involved in planning an amusement park. You need to design the rides, food areas, and walkways to make sure space is used effectively. It's crucial to get a grasp of how enlarging and reducing geometric figures impacts the available area. This scenario clearly illustrates how math and geometry are utilized in our everyday lives to address real challenges.
Subject Relevance
To Remember!
Enlargement of Geometric Figures
Enlarging geometric figures means creating a new figure that is proportional to the original, but with dimensions scaled up. This process is fundamental to understanding how metric properties like area and perimeter change with dimension adjustments.
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The enlarged figure keeps the same shape as the original, but its dimensions are scaled up according to a specific factor.
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The perimeter of the enlarged figure is directly proportional to the scale factor applied to the sides of the original figure.
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The area of the enlarged figure is proportional to the square of the scale factor applied to the sides.
Reduction of Geometric Figures
The reduction of geometric figures involves making a new figure that is proportionate to the original but has dimension reductions based on a scale factor. This process illustrates how metric properties change as the figure's dimensions are decreased.
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The reduced figure maintains the shape of the original but its dimensions are scaled down according to a specific factor.
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The perimeter of the reduced figure is directly proportional to the scale factor applied to the sides of the original figure.
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The area of the reduced figure is proportional to the square of the scale factor applied to the sides.
Calculating Perimeter and Area in Enlarged and Reduced Figures
When you enlarge or reduce geometric figures, it's essential to calculate the perimeter and area of the new figures to understand how these metric properties are affected by the changes in dimensions.
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To determine the perimeter of an enlarged or reduced figure, multiply the original perimeter by the scale factor.
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To calculate the area of an enlarged or reduced figure, multiply the original area by the square of the scale factor.
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Understanding these relationships is vital for applying the concepts of enlargement and reduction in real-world situations such as project design and model building.
Practical Applications
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Architecture: Architects apply the concepts of enlargement and reduction when creating blueprints and models of buildings at various scales to ensure accuracy.
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Civil Engineering: Civil engineers measure areas and perimeters of plots and structures to plan construction, utilizing enlargement and reduction techniques for different scales.
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Graphic Design: Graphic designers manipulate images by enlarging or reducing them to fit effectively across different media formats, from business cards to banners.
Key Terms
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Enlargement: The process of proportionally increasing the dimensions of a geometric figure.
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Reduction: The process of proportionally decreasing the dimensions of a geometric figure.
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Scale Factor: The figure you multiply or divide the dimensions of a shape by to enlarge or reduce it.
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Perimeter: The total length of all sides of a geometric figure.
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Area: The measurement of the surface of a geometric figure, expressed in square units.
Questions for Reflections
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How might the enlargement and reduction of geometric figures influence the materials needed for a construction project?
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In what ways can understanding scale be beneficial in careers like architecture and engineering?
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What difficulties did you face when calculating the new dimensions of enlarged or reduced figures during the practical exercise?
Geometric Construction Challenge
Now, let’s apply what you’ve learned about enlarging and reducing geometric figures!
Instructions
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Select a simple geometric figure (square, rectangle, triangle, or circle).
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Choose a scale factor to enlarge or reduce your original figure (for example, 2:1 for enlargement or 1:2 for reduction).
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Calculate the new dimensions of the figure, including perimeter and area.
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Sketch both the original and the enlarged/reduced figure on a piece of paper.
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Compare the metric properties of both figures and write a brief paragraph explaining how enlargement or reduction impacted the perimeter and area.
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Share your findings with your classmates or with the teacher.
