WARM UP

1) Find the area of a trapezoid with bases 8 and 11

and a height of 7.5.

2) Find the area of an equilateral triangle with sides 8ft.

3) An isosceles trapezoid has bases 12 and 28. The

area is 300. Find the height and the perimeter.

4) Find the area of a rhombus with a 120o angle and

sides of 6 cm.

Section 11.4

AREAS of REGULAR POLYGONS

Regular Polygons

• Think of a kaleidoscope.

• The body of a kaleidoscope is a tube and therefore the images always look inscribed in a circle.

• You can inscribe any regular polygon into a circle.

What is a regular polygon?• A regular polygon is a polygon with all equal

sides and angles.

Inscribe a Regular Polygon into a Circle

Center

Radius

Central Angle

Apothem

90o

60o

45o

APOTHEM

• The apothem is the perpendicular distance from the center of the polygon to the side.

APOTHEM

AREA of a REGULAR POLYGON

• Area = one half of the apothem and the perimeter.

A= ½ apAREA Apothem

Perimeter

SIMPLE

2) Find the area a regular octagon with

side 5 and apothem 3.

A= ½ ap

A= ½ (3)p5

5

5

55

5

5

5

3

P = 5(8)

P = 40

A= ½ (3)(40)

A= 60

MEDIUM

1) Find the area of a regular

hexagon with apothem 9 and side

length of 6 3

9

A= ½ ap

A= ½ (9)p

6(6 3)P

36 3P

6 36 3

6 3 6 3

6 3

19 36 3

2A

4.5 36 3A

162 3A

6 3

TOUGH

3) Find the area an equilateral

triangle with radius 16.

8 3

16

60o

60o30o

60o

8

A= ½ ap

A= ½ (8)p

3 16 3P

8 3

48 3P

18 48 3

2A 4 48 3A

192 3A

REAL TOUGH4) Find the area a regular

hexagon with a side of 4 3

120o60o

30o

4 3

4 3

4 3

4 3

4 3

2 32 3

A= ½ ap

6 4 3P

24 3P

2 3 3a

2 3a 6a

16 24 3

2A

3 24 3A

72 3A

PRACTICE

• Page 442

• # 2 - 8

• Classroom Exercises

• Draw Diagrams