WARM UP

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WARM UP

1. Find the area of a trapezoid with bases 8 and 11
   and a height of 7.5.
2. Find the area of an equilateral triangle with
   sides 8ft.
3. An isosceles trapezoid has bases 12 and 28. The
   area is 300. Find the height and the perimeter.
4. Find the area of a rhombus with a 120o angle and
   sides of 6 cm.

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Section 11.4

• AREAS of REGULAR POLYGONS

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Regular Polygons

• Think of a kaleidoscope.
• The body of a kaleidoscope is a tube and
  therefore the images always look inscribed in a
  circle.
• You can inscribe any regular polygon into a
  circle.

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What is a regular polygon?

• A regular polygon is a polygon with all equal
  sides and angles.

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(No Transcript)
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Inscribe a Regular Polygon into a Circle
90o
45o
Center Radius Central Angle Apothem
60o
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APOTHEM

• The apothem is the perpendicular distance from
  the center of the polygon to the side.

APOTHEM
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AREA of a REGULAR POLYGON

• Area one half of the apothem and the perimeter.
• A ½ ap

Perimeter
AREA
Apothem
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SIMPLE

• Find the area a regular octagon with side 5 and
  apothem 3.

5
5
5
A ½ ap
5
5
A ½ (3)p
A ½ (3)(40)
3
5
5
P 5(8)
A 60
5
P 40
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MEDIUM

• 1) Find the area of a regular hexagon with
  apothem 9 and side length of

A ½ ap
A ½ (9)p
9
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TOUGH

• 3) Find the area an equilateral triangle with
  radius 16.

A ½ ap
60o
A ½ (8)p
16
60o
8
60o
30o
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REAL TOUGH

• 4) Find the area a regular hexagon with a side of
  

A ½ ap
30o
120o
60o
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PRACTICE

• Page 442
• 2 - 8
• Classroom Exercises
• Draw Diagrams