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Chapter 11 Areas of Polygons and Circles

Find the area of a regular polygon. Find the area of an equilateral triangle. Chapter 11 Areas of Polygons and Circles. Section 11.2 Area of Regular Polygons. Lesson 1 Contents. Example 1 Area Equilateral Triangle Example 2 Area Regular Pentagon Example 3 Area Regular Octagon

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Chapter 11 Areas of Polygons and Circles

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  1. Find the area of a regular polygon Find the area of an equilateral triangle Chapter 11Areas of Polygons and Circles Section 11.2 Area of Regular Polygons

  2. Lesson 1 Contents Example 1Area Equilateral Triangle Example 2Area Regular Pentagon Example 3Area Regular Octagon Example 4Always, Sometimes, Or Never CA Standard 12.0 Students find and use measures of sides and of interior and exterior angles of triangles and polygonsto classify figures and solve problems. (Key)

  3. Find the area of an equilateral triangle 30° 60° 60°

  4. Find the area of an equilateral triangle

  5. Find the area of an equilateral triangle Answer: The triangle has area of square units Example 1-1a Find the area of the triangle The Triangle is equilateral with s = 11 Area Equilateral  s = 11 Simplify

  6. Find the area of an equilateral triangle Answer: The triangle has area of square units You 1 Find the area of the triangle

  7. 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

  8. 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

  9. Find the area of a regular polygon 4 5 Perimeter = ns = 5(5) = 25 units

  10. Find the area of a regular polygon Example 1-3a Need to find the apothem and side length Apothem = BD Side Length = AC Look at ABC

  11. Find the area of a regular polygon Example 1-3b Find BD and AC AC = 2 sin 36 BD = cos 36

  12. Find the area of a regular polygon Example 1-3c Apothem = BD = cos 36 s = AC = 2(DC) = 2 sin 36

  13. Find the area of a regular polygon 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

  14. Find the area of a regular polygon 22.5° a 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

  15. Find the area of a regular polygon Example 1-2a Find the area of an octagon with radius 3 cm s = 6 sin 22.5 a s

  16. Find the measures of interior and exterior angles of polygons 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

  17. Example 1-4a Always Always

  18. HW # 48Pg 672-675 9-29, 30-52

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