L9.5 Welcome Back! 1
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1 L9.5 Welcome Back! 1
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4 A blast from the past... L9.5 Label the following parts: Center Radius Apothem Center angle Side 4
5 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
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? Side Center Apothem Radius Radius Center angle 6
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 Center Apothem Radius Radius Center angle 7
8 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
9 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? Only center angle Center Apothem Radius Radius Center angle 9
10 A blast from the past... L9.5 What is the measure of the center angle of a regular n gon? 10
11 A blast from the past... L9.5 What is the measure of the center angle of a regular n gon? 360 n 11
12 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 n n 12
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 4 quadrilateral Center Angle Measure n pentagon hexagon octagon nonagon decagon n gon / n 13
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? quadrilateral pentagon hexagon Center Angle Measure n octagon nonagon decagon n gon / n 14
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 quadrilateral pentagon hexagon octagon nonagon Center Angle Measure n decagon n gon / n 15
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? quadrilateral pentagon hexagon octagon nonagon Center Angle Measure n decagon n gon / n 16
17 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 or for apothem triangle n quadrilateral pentagon hexagon octagon nonagon decagon n gon Center Angle Measure / n 17
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 quadrilateral 90 5 pentagon 72 6 hexagon 60 8 octagon 45 9 nonagon decagon 36 n n gon 360 / n 18
19 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 hexagon 60 8 octagon 45 9 nonagon decagon 36 n n gon 360 / n 19
20 20
21 Example L9.5 Find the area of a regular octagon w/side length 8m. Round to nearest 10 th. 1 21
22 Example L9.5 Find the area of a regular pentagon w/radius length 18. Round to nearest 10 th. 2 22
23 Example L9.5 Find the area of a regular nonagon w/apothem 6. Round to nearest 10 th. 3 23
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. 24
25 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
26 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 26
27 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 27
28 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 28
29 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 29
30 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 30
31 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 31
32 Challenge question L9.5 Find the area of this Δ (round to 10 th ): B 8 A C 1 32
33 Theorem 9-1 L9.5 What is the formula for the area of any Δ given SAS info? B c A b C 33
34 Theorem 9-1 L9.5 What is the formula for the area of any Δ given SAS info? B c A b C 34
35 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
36 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
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 c B h A x b C 37
38 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
39 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
40 Practice L9.5 pg 501 #
41 HW problems L9.5 Pg 500 #1 18,
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