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10 5 areas of a regular polygon

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  • 1. 10-5 Areas of Regular Polygons
  • 2. 10-5 Areas of Regular Polygons•Area of a Regular PolygonVocab:Center – in the centerRadius - to a vertexCentral angle –from 2 radiiApothem –perpendicularfrom center to side
  • 3. Areas of Regular Polygons•Area of a Regular Polygon
  • 4. Areas of Regular Polygons•Area of a Regular Polygon•Area = (area of the ∆) x (# of ∆’s)
  • 5. Areas of Regular Polygons•Area of a Regular Pentagon•Area = (area of the ∆) x (# of ∆’s)•Area = ( ½ apothem x side length) x (number of sides)
  • 6. Areas of Regular Polygons•Area of a Regular Pentagon•Area = (area of the ∆) x (# of ∆’s)•Area = ( ½ apothem x side length) x (number of sides)
  • 7. Areas of Regular Polygons•Area of a Regular Pentagon•Area = (½ apothem x side length) x (number of sides)•Area = ½ apothem x Perimeter
  • 8. Areas of Regular Polygons•Theorem 10-5•The area of a regular n-gon with side length s ishalf the product of the apothem a and the perimeterP•A = ½ aP•OR•A = ½ a x ns
  • 9. Areas of Regular Polygons•Area of a Regular Polygon•How to figure out the apothem
  • 10. Areas of Regular Polygons•Area of a Regular Polygon•How to figure out the apothemCBA
  • 11. Areas of Regular Polygons•Area of a Regular Polygon•How to figure out the apothem•P-Thag TheoremCBApothem
  • 12. Areas of Regular Polygons•Area of a Regular Polygon•How to figure out the apothemtan x = __B__apothemCBx°Apothem
  • 13. Areas of Regular Polygons•Area of a Regular Polygon•How to figure out the apothemtan x = __B__apothemApothem =_ B__tan xCBx°Apothem
  • 14. Areas of Regular Polygons•Area of a Regular Polygon•How to figure out the apothemcos x = apothemCApothem = cos xCCBx°Apothem
  • 15. SPICSAP 443 1-12all,14,16