10 5 areas of a regular polygon
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Transcript of 10 5 areas of a regular polygon
10-5 Areas of Regular Polygons
10-5 Areas of Regular Polygons
•Area of a Regular Polygon
Vocab:Center – in the centerRadius - to a vertexCentral angle –from 2 radiiApothem –perpendicular from center to side
Areas of Regular Polygons
•Area of a Regular Polygon
Areas of Regular Polygons
•Area of a Regular Polygon•Area = (area of the ) x (# of ’s)
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)
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)
Areas of Regular Polygons
•Area of a Regular Pentagon•Area = (½ apothem x side length) x (number of sides)•Area = ½ apothem x Perimeter
Areas of Regular Polygons
•Theorem 10-5•The area of a regular n-gon with side length s is half the product of the apothem a and the perimeter P
•A = ½ aP
•OR
•A = ½ a x ns
Areas of Regular Polygons
•Area of a Regular Polygon•How to figure out the apothem
Areas of Regular Polygons
•Area of a Regular Polygon•How to figure out the apothem
C
B
A
Areas of Regular Polygons
•Area of a Regular Polygon•How to figure out the apothem•P-Thag Theorem
C
B
Apoth
em
Areas of Regular Polygons
•Area of a Regular Polygon•How to figure out the apothem
tan x = __B__ apothem
C
B
x°
Apoth
em
Areas of Regular Polygons
•Area of a Regular Polygon•How to figure out the apothem
tan x = __B__ apothem
Apothem =_ B__ tan x
C
B
x°
Apoth
em
Areas of Regular Polygons
•Area of a Regular Polygon•How to figure out the apothem
cos x = apothem C
Apothem = cos x C
C
B
x°
Apoth
em
SPICSAP 443 1-12all,
14,16