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Understanding Perimeters and Areas of Similar Figures

In this lesson, we explore the relationships between the perimeters and areas of similar figures using the similarity ratio. Theorem 8-6 illustrates that if two figures are similar, the ratio of their perimeters is equal to the similarity ratio and the ratio of their areas is equal to the square of the similarity ratio. Through various examples, including trapezoids, polygons, and regular pentagons, we practice finding these ratios. Understanding these concepts is essential for solving problems related to geometric figures.

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Understanding Perimeters and Areas of Similar Figures

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  1. Chapter 8 Lesson 6 Objective: To find the perimeters and areas of similar figures.

  2. Theorem 8-6   Perimeters and Areas of Similar Figures If the similarity ratio of two similar figures is    , then (1) the ratio of their perimeters is   and (2) the ratio of their areas is    .

  3. Example 1: Finding Ratios in Similar Figures • The trapezoids are similar. The ratio of the lengths of corresponding sides is • Find the ratio (smaller to larger) of the perimeters. • Find the ratio (smaller to larger) of the areas.

  4. Example 2: Finding Ratios in Similar Figures Two similar polygons have corresponding sides in the ratio 5 : 7. Find the ratio of their perimeters.

  5. Example 3: Finding Ratios in Similar Figures Two similar polygons have corresponding sides in the ratio 5 : 7. Find the ratio of their areas.

  6. Example 4: Finding Areas Using Similar Figures The area of the smaller regular pentagon is about 27.5 cm2. Find the area A of the larger regular pentagon. All regular pentagons are similar. Ratio of the lengths of the corresponding sides is   The ratio of the areas is 172 cm2

  7. Example 5: Finding Areas Using Similar Figures The corresponding sides of two similar parallelograms are in the ratio ¾. The area of the larger parallelogram is 96 in.2. Find the area of the smaller parallelogram. Area Ratio

  8. Example 6: Finding Similarity and Perimeter Ratios The areas of two similar triangles are 50 cm2 and 98 cm2. What is the similarity ratio? What is the ratio of their perimeters? Find the similarity ratio a : b.

  9. Example 7: Finding Similarity and Perimeter Ratios The areas of two similar rectangles are 1875 ft2 and 135 ft2. Find the ratio of their perimeters.

  10. Assignment

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