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10 5 areas of a regular polygon

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10 5 areas of a regular polygon

1. 1. 10-5 Areas of Regular Polygons
2. 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. 3. Areas of Regular Polygons•Area of a Regular Polygon
4. 4. Areas of Regular Polygons•Area of a Regular Polygon•Area = (area of the ∆) x (# of ∆’s)
5. 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. 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. 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. 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. 9. Areas of Regular Polygons•Area of a Regular Polygon•How to figure out the apothem
10. 10. Areas of Regular Polygons•Area of a Regular Polygon•How to figure out the apothemCBA
11. 11. Areas of Regular Polygons•Area of a Regular Polygon•How to figure out the apothem•P-Thag TheoremCBApothem
12. 12. Areas of Regular Polygons•Area of a Regular Polygon•How to figure out the apothemtan x = __B__apothemCBx°Apothem
13. 13. Areas of Regular Polygons•Area of a Regular Polygon•How to figure out the apothemtan x = __B__apothemApothem =_ B__tan xCBx°Apothem
14. 14. Areas of Regular Polygons•Area of a Regular Polygon•How to figure out the apothemcos x = apothemCApothem = cos xCCBx°Apothem
15. 15. SPICSAP 443 1-12all,14,16