10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010
10.2 and 10.3 Areas of Kites, Rhombuses & Regular Polygons
Objective: Find the areas of these shapes.
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10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010
Warm­up
Find the height a of each triangle. Then find the area.
30o
2.
1.
a
a
o
18
25
10
Mar 28­5:20 PM
2
10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons Kites
B
A
E
D
March 31, 2010
C
What is the definition of a kite?
How do you think we can find the area of a kite?
What dimensions do we need to use your method?
Mar 28­3:07 PM
3
10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010
Kites B
A
E
What do you know about ΔABD and ΔCBD?
C
How would you find the area of ΔCBD in terms of the lengths AC and BD?
D
Mar 28­3:15 PM
4
10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010
Kites All we need to find the area of a kite is the length of both diagonals!!!!
B
A
E
C
Akite = ½(d1 d2)
D
d1 = AC
d2 = BD
Mar 28­3:38 PM
5
10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010
Rhombuses
C
What is a rhombus?
A
D
B
E
How do we find the area of a rhombus?
Mar 28­3:44 PM
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10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010
Rhombuses All we need to find the area of a rhombus is the length of both diagonals!!!!
D
C
E
A
Arhombus = ½(d1 d2)
B
d1 = AC
d2 = DB
Mar 28­3:45 PM
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10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010
Example #1: Find the area of the kite.
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10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010
Example #2: Find the area of the rhombus.
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10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010
Area of a Regular Polygon
What does it mean for a polygon to be regular?
How many sides does each polygon have?
pentagon:
octagon:
hexagon:
nonagon:
decagon:
Mar 28­4:13 PM
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10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010
Area of a Regular Polygon
What shape do we know how to find the area of, that we can split these regular polygons into?
Mar 28­4:17 PM
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10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010
Area of a Regular Polygon
What is the measure of angle 1?
What is the measure of angle 2?
1
2
What is the measure of angle 3?
3
Mar 28­4:33 PM
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10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010
Area of a Regular Polygon
How do we find the height a?
How do we find the area of ΔABC?
B
36o
a
What is the area of the pentagon?
54o
A
6
C
Mar 28­4:48 PM
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10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010
Area of a Regular Polygon
We found the area of ΔABC and then multiplied by the number of triangles in our shape.
Areapolygon = Areatriangle x (# of sides)
B
Areapolygon = 12 a(base)(# of sides)
36o
a
54o
A
6
C
Areapolygon = 12 ap
where a = apothem
p = perimeter
so you know: AB is called the radius
Mar 28­4:56 PM
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10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010
Example #3: What are the measures of angles 1 and 2?
1
1
2
2
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10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010
Example #4: Find the area of the decagon.
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10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010
Example #5: Find the area of the hexagon.
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10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010
Homework
Pg. 543 #11 ­ 16, 30 ­ 32
Pg. 548 # 4 ­ 18 even, 29
In many directions it says, "leave in simplest radical form". Don't worry about this, just round your answer to the nearest tenth.
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