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...
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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
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