The Scaling Principle for Area
Complete parts (i)–(iii) of the table for each of the figures in questions (a)–(d): (i) Determine the area of the figure (preimage), (ii) determine the scaled dimensions of the figure based on the provided scale factor, and (iii) determine the area of the dilated figure. Then, answer the question that follows. In the final column of the table, find the value of the ratio of the area of the similar figure to the area of the original figure. e. Make a conjecture about the relationship between the areas of the original figure and the similar figure with respect to the scale factor between the figures.
THE SCALING PRINCIPLE FOR TRIANGLES: If similar triangles 𝑆 and 𝑇 are related by a scale factor of 𝑟, then the respective areas are related by a factor of 𝑟2.
THE SCALING PRINCIPLE FOR POLYGONS: If similar polygons 𝑃 and 𝑄 are related by a scale factor of 𝑟, then their respective areas are related by a factor of 𝑟2.
THE SCALING PRINCIPLE FOR AREA: If similar figures 𝐴 and 𝐵 are related by a scale factor of 𝑟, then their respective areas are related by a factor of 𝑟2.
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.