11 4 Areas Of Regular Polygons

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11 4 Areas Of Regular Polygons

  1. 1. 11-4 Areas of Regular Polygons
  2. 2. 11.4 Areas of Regular Polygons <ul><li>Area of a Regular Polygon </li></ul>Vocab : Center – in the center Radius - to a vertex Central angle –from 2 radii Apothem –perpendicular from center to side
  3. 3. Areas of Regular Polygons <ul><li>Area of a Regular Polygon </li></ul>
  4. 4. Areas of Regular Polygons <ul><li>Area of a Regular Polygon </li></ul><ul><ul><li>Area = (area of the  ) x (# of  ’s) </li></ul></ul>
  5. 5. Areas of Regular Polygons <ul><li>Area of a Regular Pentagon </li></ul><ul><ul><li>Area = (area of the  ) x (# of  ’s) </li></ul></ul><ul><ul><li>Area = ( ½ apothem x side length) x (number of sides) </li></ul></ul>
  6. 6. Areas of Regular Polygons <ul><li>Area of a Regular Pentagon </li></ul><ul><ul><li>Area = (area of the  ) x (# of  ’s) </li></ul></ul><ul><ul><li>Area = ( ½ apothem x side length) x (number of sides) </li></ul></ul>
  7. 7. Areas of Regular Polygons <ul><li>Area of a Regular Pentagon </li></ul><ul><ul><li>Area = (½ apothem x side length) x (number of sides) </li></ul></ul><ul><ul><li>Area = ½ apothem x Perimeter </li></ul></ul>
  8. 8. Areas of Regular Polygons <ul><li>Theorem 11.6 </li></ul><ul><ul><li>The area of a regular n-gon with side length s is half the product of the apothem a and the perimeter P </li></ul></ul><ul><ul><li>A = ½ aP </li></ul></ul><ul><ul><li>OR </li></ul></ul><ul><ul><li>A = ½ a x ns </li></ul></ul>
  9. 9. Areas of Regular Polygons <ul><li>Area of a Regular Polygon </li></ul><ul><ul><li>How to figure out the apothem </li></ul></ul>
  10. 10. Areas of Regular Polygons <ul><li>Area of a Regular Polygon </li></ul><ul><ul><li>How to figure out the apothem </li></ul></ul>C B A
  11. 11. Areas of Regular Polygons <ul><li>Area of a Regular Polygon </li></ul><ul><ul><li>How to figure out the apothem </li></ul></ul><ul><ul><li>P-Thag Theorem </li></ul></ul>C B Apothem
  12. 12. Areas of Regular Polygons <ul><li>Area of a Regular Polygon </li></ul><ul><ul><li>How to figure out the apothem </li></ul></ul><ul><ul><li>tan x = __ B__ </li></ul></ul><ul><ul><li> apothem </li></ul></ul>C B x ° Apothem
  13. 13. Areas of Regular Polygons <ul><li>Area of a Regular Polygon </li></ul><ul><ul><li>How to figure out the apothem </li></ul></ul><ul><ul><li>tan x = __ B__ </li></ul></ul><ul><ul><li> apothem </li></ul></ul><ul><ul><li>Apothem =_ B__ </li></ul></ul><ul><ul><li> tan x </li></ul></ul>C B x ° Apothem
  14. 14. Areas of Regular Polygons <ul><li>Area of a Regular Polygon </li></ul><ul><ul><li>How to figure out the apothem </li></ul></ul><ul><ul><li>cos x = apothem </li></ul></ul><ul><ul><li> C </li></ul></ul><ul><ul><li>Apothem = cos x </li></ul></ul><ul><ul><li> C </li></ul></ul>C B x ° Apothem
  15. 15. SPICSA P 443 1-12all, 14,16

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