Chapter 11 Areas of Polygons and Circles

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Chapter 11Areas of Polygons and Circles

• Section 11.3
• Perimeter and Area of Similar Figures

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Lesson 1 Contents
Example 1 Finding Perimeter and Area
Ratios Example 2 Finding Area of Similar
Polygons Example 3 Finding Area of Similar
Polygons Example 4 Estimating Costs using area
CA Standard 12.0 Students find and use
measures of sides and of interior and exterior
angles of triangles and polygons to classify
figures and solve problems. (Key)
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(No Transcript)
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Example 1-1a
Pentagons ABCDE and LMNPQ are similar. a. Find
the ratio (red to blue) of the perimeters of the
pentagons. b. Find the ratio (red to blue) of
the areas of the pentagons.
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Example 1-1a
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You 1
?ABC ?DEF, Find the ratio of the perimeters and
areas
Perimeter Ratio
Area Ratio
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You 1

1. The ratio of the lengths of corresponding sides
   of two similar polygons is 37. What is the ratio
   of their areas?
2. The ratio of the areas of two similar triangles
   is 3224. What is the ratio of the lengths of
   corresponding sides?
3. A regular hexagon has an area of 60 square
   centimeters. Find the scale factor of this
   hexagon to a similar hexagon that has an area of
   240 square centimeters.

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Example 1-2a
Two similar polygons have perimeters 7 cm and 28
cm respectively. Find the area of the smaller
figure if the area of the larger is 48 cm2.
Perimeter ratio squared is the ratio of the areas
The area of the smaller polygon is 3 cm2
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Example 1-3a
The ratio of the lengths of corresponding sides
of two similar triangles is 512. The smaller
triangle has an area of 24 square centimeters.
What is the area of the larger triangle?
Scale Factor squared is the ratio of the areas
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You 2
The ratio of the lengths of corresponding sides
of two similar hexagons is 46.

1. The smaller one has a perimeter of 24
   centimeters. What is the perimeter of the larger
   hexagon?
2. The larger one has an area of square
   centimeters. What is the area of the smaller
   hexagon?

Answer 36 cm Area 1125 tan 36 ? 817.4 Square
UnitsPerimeter 150 tan 36 ? 109 Units
Answer cm2 Perimeter 150 tan 36 ? 109
Units
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Example 1-4a
COMPARING COSTS You are buying photographic paper
to print a photo in different sizes. An 8 inch by
10 inch sheet of the paper costs .42. What is a
reasonable cost for a 16 inch by 20 inch sheet?
Side ratio squared is the Area ratio
Set up a proportion relating the area to the cost
A reasonable price would be about 1.68
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You 3
A rectangular tablecloth is 60 in. by 120 in. A
rectangular place mat made from the same cloth is
12 in. by 24 in. and costs 5. Compare the areas
of the place mat and tablecloth to find a
reasonable cost for the tablecloth.
Answer 125 1125 tan 36 ? 817.4 Square
UnitsPerimeter 150 tan 36 ? 109 Units
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HW 51Pg 679-680 11-21, 23-29, 31-41