11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel =...
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Transcript of 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel =...
![Page 1: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/1.jpg)
11.1
Areas of Polygons
![Page 2: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/2.jpg)
Area of a Square = _______________________
Area of a Rectangel = ____________________
Postulate 18: ___________________________
_______________________________________
![Page 3: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/3.jpg)
If we are finding the area of a shape we do not know:
•__________________________________
•__________________________________
•__________________________________
3 2 4
2
10
![Page 4: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/4.jpg)
Classify as True or False:
1. If 2 figures have the same area then they
must be congruent.
2. If 2 fingures have the same perimeter, they
have same area.
3. If two figures are congruent they have same area.
4. Every square is a rectangle.
5. Every rectangle is a square.
6. The base of a rectangle can be any side.
![Page 5: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/5.jpg)
Examples:
30
60
Find the Area of the rectangle.
Find the Area of the square.
14
![Page 6: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/6.jpg)
11.3
Areas of ParallelogramsTriangles and Rhombuses
![Page 7: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/7.jpg)
Area of a Parallelogram= ________________
Area of a Triangle = ____________________
Area of a Rhombus = __________________
Formulas
![Page 8: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/8.jpg)
Hint : file this one away. __________________________________
__________________________________
__________________________________
Examples: Find the Area
1. Rhombus with Diagonals of 6 & 8.
2. Triangle with a base of 6 and height of 10.
![Page 9: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/9.jpg)
3. Rhombus with a Perimeter of 52 and a diagonal of 24.
4. Parallelogram with sides of 10 and 20
45
20
10
24
12
![Page 10: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/10.jpg)
5. Find the area of an isosceles triangle with congruent sides of 4 and a base of 2.
4
2
4
![Page 11: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/11.jpg)
108
Find the Area:
![Page 12: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/12.jpg)
135
5
Find the Area:
![Page 13: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/13.jpg)
11.3
Areas of Trapezoids
![Page 14: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/14.jpg)
What was a Trapezoid?
______________________________
What was the median?
______________________________
Area Trapezoid: ____________________
__________________________________
![Page 15: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/15.jpg)
Examples:
60
8
10
15
![Page 16: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/16.jpg)
A trapezoid has an area of 75 and a height of 5. How long is the median?
Which formula?
![Page 17: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/17.jpg)
Examples:
60
8
8
8
![Page 18: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/18.jpg)
2
45
3 2
Find the Area:
![Page 19: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/19.jpg)
Examples:
30
18
30
30
![Page 20: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/20.jpg)
11.4
Areas of REGULAR Polygons
![Page 21: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/21.jpg)
Think of all REGULAR polygons as being inscribed in a circle.
![Page 22: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/22.jpg)
Definitions:
Center: ______________________________
Radius : _____________________________
_____________________________________
Central Angle : _______________________
Central Angle : _______________________
_____________________________________
![Page 23: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/23.jpg)
Area of Regular Polygon= _____________
___________________________________
What Shapes can we use this for?
____________________________________________________________________________________________________________
![Page 24: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/24.jpg)
Finding the Central Angle is important because in some polygons it will form special triangles with the Radius and Apothem (ie 45-45-90 or 30-60-90)
Central Angle = _______________________
![Page 25: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/25.jpg)
CA=______ CA=_____ CA=______
![Page 26: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/26.jpg)
Examples:
1. Find the Area of a Regular hexagon with an apothem of 6.
![Page 27: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/27.jpg)
r a P A
1)
2)
5 2
3
Complete the Chart for a Square:
45
45
ar
½ side
![Page 28: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/28.jpg)
r a P A
1)
2)
8
6 3
Complete the Chart for a Triangle:
Complete the Chart for a Hexagon:
r a P A
1)
2) 24 3
8
![Page 29: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/29.jpg)
11.5
Circumference and Areas of Circles
![Page 30: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/30.jpg)
Formulas:
![Page 31: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/31.jpg)
Examples:
1. The radius of circle A is 3 times the radius of circle B. Compare the circumferences of circle A to circle B.
2. Now compare the Areas of A to B
![Page 32: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/32.jpg)
r D C A
1)
2)
3)
4)
Fill out the Chart for circle M.
15
8
26100
![Page 33: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/33.jpg)
3.The diameter of the world’s largest circle is 16m. Find the circumferences of the crust.
![Page 34: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/34.jpg)
11.6
Arc lengths andAreas of Sectors
![Page 35: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/35.jpg)
Sector: _____________________________
____________________________________
__________________________________
__________________________________
![Page 36: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/36.jpg)
Formulas:
O
B
A
![Page 37: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/37.jpg)
1.The radius of a circle is 3, and the central angle is 50.
Find the length of the arc:
Find the area of the sector:
![Page 38: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/38.jpg)
2.The area of a sector of a circle is and the central angle is 9 degrees. Find the radius of the circle
5
8
![Page 39: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/39.jpg)
Find the area of the shaded region:
6
120
![Page 40: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/40.jpg)
11.7
Ratios of Areas
![Page 41: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/41.jpg)
We will be comparing areas of figures by comparing ratios:
Case 1:
A
B
CDx z
ABD to DBCCompare
![Page 42: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/42.jpg)
We will be comparing areas of figures by comparing ratios:
Case 2:
A
B
C
D
kh
ABC to DCCompare A
![Page 43: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/43.jpg)
Case 3: If triangles are similar then:
______________________________________
Recap:
1. If heights the same then:
___________________________________
2. If Bases the same then:
___________________________________
3. If Triangles are similar then:
___________________________________
![Page 44: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/44.jpg)
Examples:
A D C
B
6
12 3
Compare the Ratios of areas between:
ABC
ADB
![Page 45: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/45.jpg)
If the scale factor of 2 similar figures is a:b then:
1. the ratio of the perimeters is_______
2. The ratio of the areas is_______
If the scale factor of 2 similar figures is 3:5 then:
1. the ratio of the perimeters is_______
2. The ratio of the areas is_______
![Page 46: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/46.jpg)
1. The diameters of 2 circles is 10 and 9. What is the ratio of their circumferences and Areas?
Ratio of Circumferences=_______
Ratio of Areas=_______________
![Page 47: 11.1 Areas of Polygons. Area of a Square = _______________________ Area of a Rectangel = ____________________ Postulate 18: ___________________________.](https://reader031.fdocuments.net/reader031/viewer/2022012919/5697bfba1a28abf838ca06c4/html5/thumbnails/47.jpg)
2. A pentagon with sides of 5,7,8,9 and 11 has an Area of 96. Find the perimeter of a similar pentagon whose Area is 24.