Chapter 11 Areas of Polygons and Circles

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Chapter 11Areas of Polygons and Circles

• Section 11.2
• Area of Regular Polygons

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Lesson 1 Contents
Example 1 Area Equilateral Triangle Example 2
Area Regular Pentagon Example 3 Area Regular
Octagon Example 4 Always, Sometimes, Or Never
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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Example 1-1a
Find the area of the triangle
The Triangle is equilateral with s 11
Area Equilateral ?
s 11
Simplify
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You 1
Find the area of the triangle
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Center of circumscribed circle
Radius of circumscribed circle
Vertex is on the center, Sides connect
consecutive vertices
Distance from center to any side of the polygons
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To find the area of the hexagon, find the area of
one triangle and multiply by 6
Height of the triangle is an apothem of the
hexagon
Base of the triangle is a side of the hexagon
6 is the number of sides of the hexagon
h
b
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Perimeter ns 5(5) 25 units
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Example 1-3a
Need to find the apothem and side length
Apothem BD
Side Length AC
Look at ?ABC
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Example 1-3b
Find BD and AC
AC 2 sin 36
BD cos 36
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Example 1-3c
Apothem BD cos 36
s AC 2(DC) 2 sin 36
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Example 1-2a
Find the area of an octagon with radius 3 cm
Need to find the apothem and side length
This angle is half the Central Angle 45 ? 2
22.5
Central Angle has measure 360 ? 8 45
This length is half of s
a
s
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Example 1-2a
Find the area of an octagon with radius 3 cm
Need to find a and s using the triangle
s 6 sin 22.5
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Example 1-2a
Find the area of an octagon with radius 3 cm
s 6 sin 22.5
a
s
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You 2
Find the Area and Perimeter of the following
pentagon
Answer Area 1125 tan 36 ? 817.4 Square
UnitsPerimeter 150 tan 36 ? 109 Units
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Example 1-4a
Always
Always
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HW 48Pg 672-675 9-29, 30-52