Upload
others
View
10
Download
0
Embed Size (px)
Citation preview
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.
10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons
2
March 31, 2010
Mar 285:20 PM
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
3
March 31, 2010
Mar 283:07 PM
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
4
March 31, 2010
Mar 283:15 PM
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
5
March 31, 2010
Mar 283:38 PM
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
10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons
6
March 31, 2010
Mar 283:44 PM
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
7
March 31, 2010
Mar 283:45 PM
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
10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons
8
March 31, 2010
Mar 284:07 PM
Example #1: Find the area of the kite.
10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons
9
March 31, 2010
Mar 284:11 PM
Example #2: Find the area of the rhombus.
10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons
10
March 31, 2010
Mar 284:13 PM
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:
10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons
11
March 31, 2010
Mar 284:17 PM
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
12
March 31, 2010
Mar 284:33 PM
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
10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons
13
March 31, 2010
Mar 284:48 PM
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
10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons
14
March 31, 2010
Mar 284:56 PM
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
10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons
15
March 31, 2010
Mar 285:14 PM
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
16
March 31, 2010
Mar 285:44 PM
Example #4: Find the area of the decagon.
10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons
17
March 31, 2010
Mar 285:46 PM
Example #5: Find the area of the hexagon.