Chapter 8 Lesson 6

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Chapter 8 Lesson 6

• Objective To find the perimeters and areas of
  similar figures.

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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    .
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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.
  

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Example 2 Finding Ratios in Similar Figures
Two similar polygons have corresponding sides in
the ratio 5 7. Find the ratio of their
perimeters.
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Example 3 Finding Ratios in Similar Figures
Two similar polygons have corresponding sides in
the ratio 5 7. Find the ratio of their areas.
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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
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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
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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.                                   
                                        
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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.
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Assignment
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