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
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Theorem 10.6
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(No Transcript)
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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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Example 4 Using Ratios to Find Perimeters and
Areas
Given that ?LMN?QRT, find the perimeter P and
area A of ?QRS.
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Example 4 Continued
Perimeter Area
13P 36(9.1)
132A (9.1)2(60)
P 25.2
A 29.4 cm2
The perimeter of ?QRS is 25.2 cm, and the area is
29.4 cm2.
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Check It Out! Example 4
?ABC ?DEF, BC 4 mm, and EF 12 mm. If P 42
mm and A 96 mm2 for ?DEF, find the perimeter
and area of ?ABC.
Perimeter Area
12P 42(4)
122A (4)2(96)
P 14 mm
The perimeter of ?ABC is 14 mm, and the area is
10.7 mm2.
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Lesson Quiz Part I
1. Maria is 4 ft 2 in. tall. To find the height
of a flagpole, she measured her shadow and the
poles shadow. What is the height h of the
flagpole? 2. A blueprint for Latishas bedroom
uses a scale of 1 in.4 ft. Her bedroom on the
blueprint is 3 in. long. How long is the actual
room?
25 ft
12 ft
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Lesson Quiz Part II
3. ?ABC ?DEF. Find the perimeter and area of
?ABC.
P 27 in., A 31.5 in2
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Homework

• P. 527 1-22 not 8 or 13