11-2: Areas of Parallelograms, Triangles, and...
Transcript of 11-2: Areas of Parallelograms, Triangles, and...
![Page 1: 11-2: Areas of Parallelograms, Triangles, and Rhombusesmrleongeometry.weebly.com/uploads/5/7/6/8/57684959/11-2... · 2016-03-08 · of parallelograms, triangles, and rhombuses. ...](https://reader031.fdocuments.in/reader031/viewer/2022021823/5b3756987f8b9a4a728bf76e/html5/thumbnails/1.jpg)
11-2: Areas of Parallelograms, Triangles, and Rhombuses
![Page 2: 11-2: Areas of Parallelograms, Triangles, and Rhombusesmrleongeometry.weebly.com/uploads/5/7/6/8/57684959/11-2... · 2016-03-08 · of parallelograms, triangles, and rhombuses. ...](https://reader031.fdocuments.in/reader031/viewer/2022021823/5b3756987f8b9a4a728bf76e/html5/thumbnails/2.jpg)
We are going to finish up the examples from
yesterday.
Refer to the 11-1 Presentation for solutions
to those problems.
![Page 3: 11-2: Areas of Parallelograms, Triangles, and Rhombusesmrleongeometry.weebly.com/uploads/5/7/6/8/57684959/11-2... · 2016-03-08 · of parallelograms, triangles, and rhombuses. ...](https://reader031.fdocuments.in/reader031/viewer/2022021823/5b3756987f8b9a4a728bf76e/html5/thumbnails/3.jpg)
Content Objective: Students will be able to
use postulates and theorems to find the area
of parallelograms, triangles, and rhombuses.
Language Objective: Students will be able to
identify polygons and their appropriate area
formulas.
![Page 4: 11-2: Areas of Parallelograms, Triangles, and Rhombusesmrleongeometry.weebly.com/uploads/5/7/6/8/57684959/11-2... · 2016-03-08 · of parallelograms, triangles, and rhombuses. ...](https://reader031.fdocuments.in/reader031/viewer/2022021823/5b3756987f8b9a4a728bf76e/html5/thumbnails/4.jpg)
Estimate the are using square units. Explain how you
found it quickly (i.e. not just “counting squares”)
Just take a Guess.
No right or wrong with
this one.
![Page 5: 11-2: Areas of Parallelograms, Triangles, and Rhombusesmrleongeometry.weebly.com/uploads/5/7/6/8/57684959/11-2... · 2016-03-08 · of parallelograms, triangles, and rhombuses. ...](https://reader031.fdocuments.in/reader031/viewer/2022021823/5b3756987f8b9a4a728bf76e/html5/thumbnails/5.jpg)
Theorem 11-2: The area of a parallelogram equals the product of a base and the height to that base.
Equation: 𝐴 = 𝑏ℎ
b
h
![Page 6: 11-2: Areas of Parallelograms, Triangles, and Rhombusesmrleongeometry.weebly.com/uploads/5/7/6/8/57684959/11-2... · 2016-03-08 · of parallelograms, triangles, and rhombuses. ...](https://reader031.fdocuments.in/reader031/viewer/2022021823/5b3756987f8b9a4a728bf76e/html5/thumbnails/6.jpg)
Estimate the are using square units. Explain how you
found it quickly (i.e. not just “counting squares”)
![Page 7: 11-2: Areas of Parallelograms, Triangles, and Rhombusesmrleongeometry.weebly.com/uploads/5/7/6/8/57684959/11-2... · 2016-03-08 · of parallelograms, triangles, and rhombuses. ...](https://reader031.fdocuments.in/reader031/viewer/2022021823/5b3756987f8b9a4a728bf76e/html5/thumbnails/7.jpg)
Theorem 11-3: The area of a triangle equals half the product
of a base and the height to that base.
Equation: 𝐴 =1
2𝑏ℎ
b
h
![Page 8: 11-2: Areas of Parallelograms, Triangles, and Rhombusesmrleongeometry.weebly.com/uploads/5/7/6/8/57684959/11-2... · 2016-03-08 · of parallelograms, triangles, and rhombuses. ...](https://reader031.fdocuments.in/reader031/viewer/2022021823/5b3756987f8b9a4a728bf76e/html5/thumbnails/8.jpg)
Estimate the are using square units. Explain how you
found it quickly (i.e. not just “counting squares”)
![Page 9: 11-2: Areas of Parallelograms, Triangles, and Rhombusesmrleongeometry.weebly.com/uploads/5/7/6/8/57684959/11-2... · 2016-03-08 · of parallelograms, triangles, and rhombuses. ...](https://reader031.fdocuments.in/reader031/viewer/2022021823/5b3756987f8b9a4a728bf76e/html5/thumbnails/9.jpg)
Theorem 11-4: The area of a Rhombus equals half the product
of its diagonals.
Equation: 1
2𝑑1𝑑2
![Page 10: 11-2: Areas of Parallelograms, Triangles, and Rhombusesmrleongeometry.weebly.com/uploads/5/7/6/8/57684959/11-2... · 2016-03-08 · of parallelograms, triangles, and rhombuses. ...](https://reader031.fdocuments.in/reader031/viewer/2022021823/5b3756987f8b9a4a728bf76e/html5/thumbnails/10.jpg)
Find the area of each figure.
6
6
3 3
60°
1.5 3
Solution:
Area of a Parallelogram
𝐴 = 6 × 1.5 3
𝑨 = 𝟗 𝟑
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Find the area of each figure.
Solution:
Area of a Square
𝐴 =1
2(6 × 4)
𝐴 =1
2× 24
𝑨 = 𝟏𝟐
6
5 4
3
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Find the area of each figure.
4
5
5 3
Solution:
Area of a Rhombus
𝐴 =1
2(8 × 6)
𝐴 =1
2× 48
𝑨 = 𝟐𝟒
![Page 13: 11-2: Areas of Parallelograms, Triangles, and Rhombusesmrleongeometry.weebly.com/uploads/5/7/6/8/57684959/11-2... · 2016-03-08 · of parallelograms, triangles, and rhombuses. ...](https://reader031.fdocuments.in/reader031/viewer/2022021823/5b3756987f8b9a4a728bf76e/html5/thumbnails/13.jpg)
Find the area for the following diagrams in your groups.
1.)
4
4
4 2 3
Solution:
Area of a Square
𝐴 =1
2(4 × 2 3)
𝐴 =1
2× 8 3
𝑨 = 𝟒 𝟑
![Page 14: 11-2: Areas of Parallelograms, Triangles, and Rhombusesmrleongeometry.weebly.com/uploads/5/7/6/8/57684959/11-2... · 2016-03-08 · of parallelograms, triangles, and rhombuses. ...](https://reader031.fdocuments.in/reader031/viewer/2022021823/5b3756987f8b9a4a728bf76e/html5/thumbnails/14.jpg)
Find the area for the following diagrams in your groups.
2.)
2
2
5
5
Solution:
Area of a Rhombus
𝐴 =1
2(4 × 10)
𝐴 =1
2× 40
𝑨 = 𝟐𝟎
![Page 15: 11-2: Areas of Parallelograms, Triangles, and Rhombusesmrleongeometry.weebly.com/uploads/5/7/6/8/57684959/11-2... · 2016-03-08 · of parallelograms, triangles, and rhombuses. ...](https://reader031.fdocuments.in/reader031/viewer/2022021823/5b3756987f8b9a4a728bf76e/html5/thumbnails/15.jpg)
Find the area for the following diagrams in your groups.
3.)
5 5
4 4
8
Solution:
Separate the Areas
𝐴 =1
2(8 × 3) + (8 × 4)
𝐴 = 12 + 32
𝑨 = 𝟒𝟒
3
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Find the area for the following diagrams in your groups.
4.)
5
12
13
Solution:
Area of a Square
𝐴 =1
2(12 × 5)
𝐴 =1
2× 60
𝑨 = 𝟑𝟎
![Page 17: 11-2: Areas of Parallelograms, Triangles, and Rhombusesmrleongeometry.weebly.com/uploads/5/7/6/8/57684959/11-2... · 2016-03-08 · of parallelograms, triangles, and rhombuses. ...](https://reader031.fdocuments.in/reader031/viewer/2022021823/5b3756987f8b9a4a728bf76e/html5/thumbnails/17.jpg)
Find the area for the following diagrams in your groups.
5.)
5
12
13
15 9
Solution:
Separate the Areas
𝐴 =1
2(12 × 5) +
1
2(12 × 9)
𝐴 = 30 + 54
𝑨 = 𝟖𝟒
![Page 18: 11-2: Areas of Parallelograms, Triangles, and Rhombusesmrleongeometry.weebly.com/uploads/5/7/6/8/57684959/11-2... · 2016-03-08 · of parallelograms, triangles, and rhombuses. ...](https://reader031.fdocuments.in/reader031/viewer/2022021823/5b3756987f8b9a4a728bf76e/html5/thumbnails/18.jpg)
Find the area for the following diagrams in your groups.
6.)
Solution:
Separate the Areas
𝐴 = 12 × 4 + (62)
𝐴 = 48 + 36
𝑨 = 𝟖𝟒
6 4
12
![Page 19: 11-2: Areas of Parallelograms, Triangles, and Rhombusesmrleongeometry.weebly.com/uploads/5/7/6/8/57684959/11-2... · 2016-03-08 · of parallelograms, triangles, and rhombuses. ...](https://reader031.fdocuments.in/reader031/viewer/2022021823/5b3756987f8b9a4a728bf76e/html5/thumbnails/19.jpg)
Find the area for the following diagrams in your groups.
7.) Solution:
Area of a Square
𝐴 =1
2(7 2 × 7 2)
𝐴 =1
2× 28
𝑨 = 𝟏𝟒
14
45°
𝟕 𝟐
𝟕 𝟐
![Page 20: 11-2: Areas of Parallelograms, Triangles, and Rhombusesmrleongeometry.weebly.com/uploads/5/7/6/8/57684959/11-2... · 2016-03-08 · of parallelograms, triangles, and rhombuses. ...](https://reader031.fdocuments.in/reader031/viewer/2022021823/5b3756987f8b9a4a728bf76e/html5/thumbnails/20.jpg)
Find the area for the following diagrams in your groups.
8.)
8
𝟖 𝟑
16 60°
Solution:
Area of a Square
𝐴 =1
2(8 3 × 8)
𝐴 =1
2× 64 3
𝑨 = 𝟑𝟐 𝟑
![Page 21: 11-2: Areas of Parallelograms, Triangles, and Rhombusesmrleongeometry.weebly.com/uploads/5/7/6/8/57684959/11-2... · 2016-03-08 · of parallelograms, triangles, and rhombuses. ...](https://reader031.fdocuments.in/reader031/viewer/2022021823/5b3756987f8b9a4a728bf76e/html5/thumbnails/21.jpg)
Find the area for the following diagrams in your groups.
9.)
20 50°
12.9
15.3
Solution:
Area of a Square
𝐴 =1
2(15.3 × 12.9)
𝐴 =1
2× 197.37
𝑨 = 𝟗𝟖. 𝟔𝟖𝟓