L9.5 Welcome Back! 1

A blast from the past... L9.5 Label the following parts: Center Radius Apothem Center angle Side 4

A blast from the past... L9.5 Label the following parts: Center Radius Apothem Center angle Side Center Radius Radius Center angle Side Apothem 5

A blast from the past... L9.5 Label the following parts: Center Radius Apothem Center angle Side What is the formula for the area of a regular polygon? Side Center Apothem Radius Radius Center angle 6

A blast from the past... L9.5 Label the following parts: Center Radius Apothem Center angle Side What is the formula for the area of a regular polygon? A = 1 / 2 ap Side Center Apothem Radius Radius Center angle 7

A blast from the past... L9.5 Label the following parts: Center Radius Apothem Center angle Side What is the formula for the area of a regular polygon? A = 1 / 2 ap Side Which of these parts are constant for a specific type of regular poly? Center Apothem Radius Radius Center angle 8

A blast from the past... L9.5 What is the measure of the center angle of a regular n gon? 10

A blast from the past... L9.5 What is the measure of the center angle of a regular n gon? 360 n 11

A blast from the past... L9.5 What is the measure of the center angle of a regular n gon? # Sides Poly Name Center Angle Measure 360 3 n 4 5 6 8 9 10 n 12

A blast from the past... L9.5 What is the measure of the center angle of a regular n gon? # Sides Poly Name 3 triangle 360 n 4 quadrilateral Center Angle Measure 120 90 5 6 8 9 10 n pentagon hexagon octagon nonagon decagon n gon 72 60 45 40 36 360 / n 13

A blast from the past... L9.5 What is the measure of the center angle of a regular n gon? # Sides Poly Name 3 triangle 360 n In chapter 7 we found the area of various reg polys...which of these did you work with? 4 5 6 quadrilateral pentagon hexagon Center Angle Measure 120 90 72 60 8 9 10 n octagon nonagon decagon n gon 45 40 36 360 / n 14

A blast from the past... L9.5 What is the measure of the center angle of a regular n gon? # Sides Poly Name 3 triangle 360 n In chapter 7 we found the area of various reg polys...which of these did you work with? Triangle Quad Hexagon 4 5 6 8 9 quadrilateral pentagon hexagon octagon nonagon Center Angle Measure 120 90 72 60 45 40 10 n decagon n gon 36 360 / n 15

A blast from the past... L9.5 What is the measure of the center angle of a regular n gon? # Sides Poly Name 3 triangle 360 n In chapter 7 we found the area of various reg polys...which of these did you work with? Triangle Quad Hexagon Why only those? 4 5 6 8 9 quadrilateral pentagon hexagon octagon nonagon Center Angle Measure 120 90 72 60 45 40 10 n decagon n gon 36 360 / n 16

A blast from the past... L9.5 What is the measure of the center angle of a regular n gon? # Sides Poly Name 3 triangle 360 n In chapter 7 we found the area of various reg polys...which of these did you work with? Triangle Quad Hexagon Why only those? Only ones that have 30 60 09 or 45 45 90 for apothem triangle 4 5 6 8 9 10 n quadrilateral pentagon hexagon octagon nonagon decagon n gon Center Angle Measure 120 90 72 60 45 40 36 360 / n 17

A blast from the past... L9.5 Now with the trig ratios all the rest are open to us! # Sides 3 Poly Name triangle Center Angle Measure 120 4 quadrilateral 90 5 pentagon 72 6 hexagon 60 8 octagon 45 9 nonagon 40 10 decagon 36 n n gon 360 / n 18

A blast from the past... L9.5 Now with the trig ratios all the rest are open to us! # Sides 3 Poly Name triangle Center Angle Measure 120 We can work with any center angle measure! 4 5 quadrilateral pentagon 90 72 6 hexagon 60 8 octagon 45 9 nonagon 40 10 decagon 36 n n gon 360 / n 19

Example L9.5 Find the area of a regular octagon w/side length 8m. Round to nearest 10 th. 1 21

Example L9.5 Find the area of a regular pentagon w/radius length 18. Round to nearest 10 th. 2 22

Example L9.5 Find the area of a regular nonagon w/apothem 6. Round to nearest 10 th. 3 23

How to find the area of any reg poly... L9.5 Write the steps to take in order to find the area of a regular polygon w/n sides. 24

How to find the area of any reg poly... L9.5 Write the steps to take in order to find the area of a regular polygon w/n sides. 1) Determine # sides 2) Determine center angle 3) Determine apothem 4) Determine perimeter... for any of the above * may be given * use trig ratios if not 25

Challenge question L9.5 Find the area of this Δ (round to 10 th ): B 8 A 40 11 C 1 32

Theorem 9-1 L9.5 What is the formula for the area of any Δ given SAS info? B c A b C 33

Theorem 9-1 L9.5 What is the formula for the area of any Δ given SAS info? B c A b C 34

Theorem 9-1 L9.5 What is the formula for the area of any Δ given SAS info? B c h A b C 35

Theorem 9-1 L9.5 What is the formula for the area of any Δ given SAS info? sin A = h c B c h A b C 36

Theorem 9-1 L9.5 What is the formula for the area of any Δ given SAS info? sin A = h c h = c sin A c B h A x b C 37

Theorem 9-1 L9.5 What is the formula for the area of any Δ given SAS info? sin A = h c h = c sin A area Δ = 1 / 2 bh c B h A x b C 38

Theorem 9-1 Area of a Δ given SAS info L9.5 What is the formula for the area of any Δ given SAS info? sin A = h c h = c sin A area Δ = 1 / 2 bh c B h area Δ = 1 / 2 b c sin A A x b C 39

Practice L9.5 pg 501 #11 13 40

HW problems L9.5 Pg 500 #1 18, 20 27 41