Similarity — The Relation Between the Area of Two Similar Polygons

About this lesson

This unit focuses on the relationship between the areas of similar triangles and similar polygons. It begins by exploring the ratio of areas of two similar triangles, establishing that this ratio equals the square of the similarity ratio (scale factor). The text includes a proof (though not required) and examples showing how to find areas of similar triangles and trapeziums, and how to use the ratio of areas to find perimeters. It then extends the concept to similar polygons, stating that the ratio of their areas equals the square of the ratio of corresponding sides. Worked examples involve maps, farms, and polygons, and exercises ask students to complete ratios, find missing lengths or areas, and prove relationships. By the end, students should be able to apply the area ratio theorem to solve problems involving similar triangles and polygons, including finding perimeters and areas.