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Area of Regular Polygons - PowerPoint PPT Presentation

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Area of Regular Polygons

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  1. Area of Regular Polygons

  2. We will determinethe area of regular polygons using notes.

  3. Copy onto your notes:

  4. Copy onto your notes: Regular Polygon • equal sides • equal angles P = perimeter a = apothem * Use this formula for regular pentagons, hexagons, octagons, etc.

  5. Copy onto your notes: apothem Apothem - connects center to midpoint and forms a right angle

  6. Copy onto your notes: Examples Non-Examples

  7. Copy onto your notes:

  8. You try this one now… 14 cm 2.5 cm Example 2 : Find the area of the regular octagon.

  9. Click through the animation and copy down the important information. First, divide the hexagon into 6 six congruent figures. What figures did you create? Equilateral Triangles Now, divide the hexagon into 12 congruent figures. What figures did you create? 30 – 60 – 90 Triangles Label the sides of one of the 30 – 60 – 90 Triangle. What did you label the apothem? x√3 What represents the side length? 2x

  10. Copy onto your notes:

  11. You try this one now… Example 4: Find the area of the regular hexagon with a perimeter 42 cm. (Round to the nearest tenth)

  12. Keep trying! Example 5 : The area of a regular hexagon is 54 cm2. If the perimeter of the hexagon is 48 cm, what is the length of the apothem?

  13. Keep trying! Example 6: The area of a regular nonagon is 198 mm2. If the apothem of the figure is 6 mm, what is the perimeter?

  14. Keep trying! B A C D E Example 7: The area of regular pentagon ABCDE is 92 cm2. If the apothem of the figure is 4 cm, what is the length of CD?