Perimeters and Areas of Similar Figures

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Perimeters and Areas of Similar Figures

• 10.5

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Theorem 10.6

• If the similarity ratio of two similar figures is
  ab then (1) the ratio of their perimeters is ab
  and (2) the ratio of their areas is a2b2

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Example I

• The area of the smaller figure is 27.5. Find the
  area of the larger one.
• Any two regular pentagons are similar therefore
  the corresponding sides are 4/10 or 2/5. The
  ratio of the areas is 22/52.
• 4/25 27.5/x
• Area of larger pentagon is about 172

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10
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Example II

• The area of two similar triangles are 50cm2 and
  98cm2. What is the ratio of their perimeters?
• a2/b2 50/98 (ratio of areas)
• a2/b2 25/49 (Simplify)
• a/b 5/7 (find the sq. root)
• So the ratio of the perimeters is 5/7

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Homework

• P. 527 1-20 not 8 or 13