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