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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