• Students identify the scale factor.
• Given a scale drawing, students compute the area in the actual picture.
Given the scale factor r representing the relationship between scale drawing length and actual length, the square of this scale factor, r2, represents the relationship between scale drawing area and actual area.
Examples 1–3: Exploring Area Relationships
Use the diagrams below to find the scale factor and then find the area of each figure.
Results: What do you notice about the ratio of the areas in Examples 1-3? Complete the statements below.
When the scale factor of the sides was 2, then the ratio of area was ______.
When the scale factor of the sides was 1/3, then the ratio of area was ____.
When the scale factor of the sides was 4/3, then the ratio of area was _____
Based on these observations, what conclusion can you draw about scale factor and area?
If the scale factor is r, then the ratio of area is ____
Example 4: They Said Yes!
The Student Government liked your half-court basketball plan. They have asked you to calculate the actual area of the court so that they can estimate the cost of the project.
Based on the drawing below, what is the area of the planned half-court going to be?
Does the actual area you found reflect the results we found from Examples 1–3? Explain how you know.
1. The triangle depicted by the drawing has an actual area of 36 square units. What is the scale of the drawing? (Note: each square on grid has a length of 1 unit.)
2. Use the scale drawings of two different apartments to answer the questions. Use a ruler to measure.
a. Find the scale drawing area for both apartments, and then use it to find the actual area of both apartments.
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