10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons 1 March 31, 2010 Mar 282:49 PM 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
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10.2 and 10.3 Areas of Kites, Rhombuses &
Regular Polygons
Objective: Find the areas of these shapes.
10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons
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WarmupFind the height a of each triangle. Then find the area.
1025o
a1. 2. 30o
18a
10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons
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Kites
How do you think we can find the area of a kite?What dimensions do we need to use your method?
A
B
C
D
EWhat is the definition of a kite?
10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons
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Kites
A
B
C
D
E
What do you know about ΔABD and ΔCBD?
How would you find the area of ΔCBD in terms of the lengths AC and BD?
10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons
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Kites
All we need to find the area of a kite is the length of both diagonals!!!!
Akite = ½(d1 d2)A
B
C
D
E
d1 = ACd2 = BD
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Rhombuses
A
B
C
D
E
What is a rhombus?
How do we find the area of a rhombus?
10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons
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Rhombuses All we need to find the area of a rhombus is
the length of both diagonals!!!!
Arhombus = ½(d1 d2)A B
CD
E
d1 = ACd2 = DB
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Example #1: Find the area of the kite.
10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons
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Example #2: Find the area of the rhombus.
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Area of a Regular Polygon
What does it mean for a polygon to be regular?
How many sides does each polygon have?
pentagon:
hexagon:
octagon:
nonagon:
decagon:
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Area of a Regular Polygon
What shape do we know how to find the area of, that we can split these regular polygons into?
10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons
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12
3
What is the measure of angle 1?
What is the measure of angle 2?
What is the measure of angle 3?
Area of a Regular Polygon
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36o
54oa
6A
B
C
How do we find the height a?
How do we find the area of ΔABC?
What is the area of the pentagon?
Area of a Regular Polygon
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We found the area of ΔABC and then multiplied by the number of triangles in our shape.
36o
54oa
6A
B
C
12 a(base)(# of sides)Areapolygon =
Areapolygon = Areatriangle x (# of sides)
12 apAreapolygon =
where a = apothem p = perimeter
so you know: AB is called the radius
Area of a Regular Polygon
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1
2
1
2
What are the measures of angles 1 and 2?Example #3:
10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons
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Example #4: Find the area of the decagon.
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Example #5: Find the area of the hexagon.
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Homework
Pg. 543 #11 16, 30 32Pg. 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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