Geo 10.2 day 25.notebook

Geo 10.2 day 25.notebook
April 11, 2017
Warm Ups Day 25
1) Find the Area and Circumference
2) Find the area to the nearest tenth.
(exact, and to nearest tenth)
5 in.
d = 8 in
30o
5 in.
3) Find the lower base if Area = 70 in .
2
7 in.
x
Apr 9­10:52 AM
Get Ch 7 test back.
Apr 11­10:43 AM
1
Geo 10.2 day 25.notebook
April 11, 2017
Questions on HW 24 pg 681?
Apr 9­1:21 PM
Mar 29­6:02 PM
2
Geo 10.2 day 25.notebook
April 11, 2017
Apr 9­1:22 PM
pass in
Mar 29­6:02 PM
3
Geo 10.2 day 25.notebook
April 11, 2017
10.2 GOALS
1) Develop and apply the formulas for the area and circumference of a circle.
2) Develop and apply the formula for the area of a regular polygon.
Apr 9­10:50 AM
Why is the area of a circle It all started with the discovery that ??
<­­­circumference
<­­­diameter
d
Mar 29­6:11 PM
4
Geo 10.2 day 25.notebook
April 11, 2017
­­­­>
Sep 13­5:38 PM
­­­­>
Sep 13­5:42 PM
5
Geo 10.2 day 25.notebook
April 11, 2017
­­­>
Sep 13­5:44 PM
Parallelogram!
­­­>
|­­­­­­­­­­­­­­­ 1_ C ­­­­­­­­­­­­­­­­|
2
A = 1_2 d r
1
_
A = 2 2r r
r2
A = Sep 13­5:44 PM
6
Geo 10.2 day 25.notebook
April 11, 2017
A circle is named by the symbol ¤ and its center. ¤A
or
radius AB, AD, AC diameter CD Apr 9­11:01 AM
CW 25 in groups
1) Find the area of ¤K in terms of π.
1
2) Find the radius of ¤J if the circumference is (100π )m.
3) Find the circumference of ¤M if the area is (25π)ft2
4) Find the area of ¤A in terms of π in which C = (4π) m.
Apr 9­11:06 AM
7
Geo 10.2 day 25.notebook
April 11, 2017
Break
Apr 11­1:06 PM
Vocab Notes
Center of a regular polygon
A point equidistant from the vertices.
B
Radius
A segment that connects the center to a vertex
Apothem
A
A segment that connects center to a side _|
C
D
Central Angle
An angle whose vertex is at the center and its sides pass through consecutive vertices.
Each central angle measure of a regular n­gon is Apr 12­7:41 AM
8
Geo 10.2 day 25.notebook
April 11, 2017
What is the value of one central angle of each regular polygon?
3 sides
6 sides
4 sides
7­sides
5 sides
8 sides
Apr 9­11:37 AM
Regular pentagon DEFGH Name each:
vertex
1) ∠FGH ____
central angle
2) ∠GCH ____
center
3) point C ____
apothem
4) segment BC ____
radius
5) segment CF ____
Apr 9­11:30 AM
9
Geo 10.2 day 25.notebook
April 11, 2017
Can we find the area of a regular polygon given a side length? 6 cm
Mar 29­6:36 PM
Can we find the area of a regular polygon given a side length? 6
Mar 29­6:36 PM
10
Geo 10.2 day 25.notebook
April 11, 2017
Can we find the area of a regular polygon given a side length? 6
Mar 29­6:36 PM
Can we find the area of a regular polygon given a side length? 6
Mar 29­6:36 PM
11
Geo 10.2 day 25.notebook
April 11, 2017
Can we find the area of a regular polygon given a side length? 6
173.8 cm 2
Mar 29­6:36 PM
Find the area of regular heptagon with side length 2 ft to the nearest tenth.
2 ft
Apr 9­11:31 AM
12
Geo 10.2 day 25.notebook
April 11, 2017
Finding the Area of a Regular Polygon
Find the area of regular heptagon with side length 2 ft to the nearest tenth.
Step 1 Draw the heptagon. The central angle is _____. 2 ft.
51.4o
Step 2 Draw the triangle formed by the central angle. Draw the apothem, which bisects the central angle and the side of the polygon to form a right triangle. 51.4o
2 ft.
Apr 9­12:16 PM
Step 3 Use the tangent ratio to find the apothem.
51.4o
2 ft.
51.4o
2 ft
Apr 9­12:25 PM
13
Geo 10.2 day 25.notebook
April 11, 2017
Step 4 Use the apothem and the given side length to find the area.
Apr 9­12:34 PM
Find the area of a regular dodecagon with side length 5 cm to the nearest tenth.
Step 1 Draw the dodecagon. The central angle is_____. Step 2 Draw the triangle formed by the central angle. Draw the apothem, which bisects the central angle and the side of the polygon to form a right triangle. Step 3 Use the tangent ratio to find the apothem. Step 4 Use the apothem and the given side length to find the area.
Apr 9­12:36 PM
14
Geo 10.2 day 25.notebook
April 11, 2017
Find the area of a regular dodecagon with side length 5 cm to the nearest tenth.
5 cm
Apr 9­12:38 PM
Find the area of the regular hexagon that has a distance of 15 inches from the center to the vertices. 15 in.
Apr 9­12:49 PM
15
Geo 10.2 day 25.notebook
April 11, 2017
A regular triangle with an apothem of 10 inches. Find the area of the triangle.
10 Apr 9­1:39 PM
HW 25 pg 691 #4, 6­9, 18­26, 28, 30 Apr 9­4:16 PM
16