chapter 7 lesson 5 objective: objective: to find the area of a regular polygon
TRANSCRIPT
Chapter 7 Chapter 7 Lesson 5Lesson 5
Objective:Objective: To find the area of a regular polygon
• You can You can circumscribecircumscribe a circle about any regular a circle about any regular polygon.polygon.
Regula
r
Regula
r
Polyg
on
Polyg
on
ss
• Center of a Regular PolygonCenter of a Regular Polygon is the center of the is the center of the circumscribed circle.circumscribed circle.• Radius Radius is the distance from the center to a is the distance from the center to a vertex.vertex.• ApothemApothem is the perpendicular distance from the is the perpendicular distance from the center to a sidecenter to a side
Example 1:Finding Angle Measures
11
22
33
6360
1m 60
Find the measure of each Find the measure of each numbered angle.numbered angle.
121
2 mm )60(21
30
18090303 m1801203 m
33
603 m
Example 2:Finding Angle Measures
11
33
225360
1m 72
121
2 mm )72(21
3633
Find the measure of each Find the measure of each numbered angle.numbered angle.
18090363 m1801263 m
543 m
Example 3:Finding Angle Measures
Find the measure of each Find the measure of each numbered angle.numbered angle.
1122
33
3360
1m 120
121
2 mm )120(21
60
18090603 m1801503 m
303 m
Example 4:Finding Angle Measures
11
22
33
Find the measure of each Find the measure of each numbered angle.numbered angle.
4360
1m 90
121
2 mm )90(21
45
18090453 m1801353 m
453 m
22
Theorem 7-12: Theorem 7-12: Area of a Regular PolygonThe area of a regular polygon is half the product of the apothem and the perimeter.
a
Perimeter is the measurement Perimeter is the measurement around the polygonaround the polygon
apA21
Example 5:Example 5:Finding the Area of a Regular PolygonFinding the Area of a Regular Polygon
33
6
Step 1: Step 1: Find the perimeter.# of Sides: 6
p=nsp=6(6)p=36
Step 2:Step 2: Find the area.
)36)(33(21
A
apA21
)3108(21
A
354A
Example 6:Example 6:Finding the Area of a Regular PolygonFinding the Area of a Regular Polygon
38
16
Step 1: Step 1: Find the perimeter.# of Sides: 6
p=nsp=6(16)
p=96
Step 2:Step 2: Find the area.
)96)(38(21
A
apA21
)3768(21
A
3384A
Example 7:Example 7:Finding the Area of a Regular PolygonFinding the Area of a Regular Polygon
2
4
Step 1: Step 1: Find the perimeter.# of Sides: 4
p=nsp=4(4)p=16
Step 2:Step 2: Find the area.
)16)(2(21
A
apA21
)32(21
A
16A
Example 8:Example 8:Finding the Area of a Regular PolygonFinding the Area of a Regular Polygon
310
)180)(310(2
1A
apA21
)31800(2
1A
3900A
Look at your notes from yesterday what kind of triangle do you have?
30° - 60° - 90°
60°
30°
SLLL 3
3103 LL30LL
Remember Remember that 30 is that 30 is
only half the only half the base the base the
whole base whole base is 60is 60
Find the perimeter.# of Sides: 3p=nsp=3(60)p=180
25
Example 9:Example 9:Finding the Area of a Regular PolygonFinding the Area of a Regular Polygon
)40)(5(21
A
apA21
)200(21
A
100A
Look at your notes from yesterday what kind of triangle do you have?
45° - 45° - 90°
leghyp 2.
leg 225leg5
Remember Remember that 5 is that 5 is
only half the only half the base the base the
whole base whole base is 10is 10
Find the perimeter.# of Sides: 4p=nsp=4(10)p=40
45°
45°
Example 10:Example 10:Finding the Area of a Regular PolygonFinding the Area of a Regular Polygon
)36)(32(2
1A
apA21
)372(2
1A
336A
Look at your notes from yesterday what kind of triangle do you have?
30° - 60° - 90°
60°
30°
SLLL 3
SL 36
SL3
6
Remember Remember LL is your LL is your apothem.apothem.
Find the perimeter.# of Sides: 3p=nsp=3(12)p=36
1212
66 66
SL32
AssignmenAssignment:t:
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