which of the following areas are you trying to find? parallelogramtriangletrapezoid areas of...
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Which of the following areas are you trying to find?
Parallelogram Triangle Trapezoid
AREAS OF POLYGONS
![Page 2: Which of the following areas are you trying to find? ParallelogramTriangleTrapezoid AREAS OF POLYGONS](https://reader033.vdocuments.net/reader033/viewer/2022051415/56649d005503460f949d1957/html5/thumbnails/2.jpg)
AREA OF A PARALLELOGRAM
Welcome. Today you’re going to discover the formula for area of a parallelogram.
h
b
Click to Continue
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AREA OF A PARALLELOGRAM
To do this let’s cut the left triangle and…
h
b
Click to Continue
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slide it…
AREA OF A PARALLELOGRAM
h
h b
Click to Continue
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slide it…
AREA OF A PARALLELOGRAM
h
h
b
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slide it…
AREA OF A PARALLELOGRAM
h
h
b
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slide it…
AREA OF A PARALLELOGRAM
h
hb
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…thus, changing it to a rectangle.
What is the area of the rectangle?
AREA OF PARALLELOGRAM
h
b
bhA hbA bhA 2
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Congratulations!!!
You Answered Correctly.
Click to continue.
![Page 10: Which of the following areas are you trying to find? ParallelogramTriangleTrapezoid AREAS OF POLYGONS](https://reader033.vdocuments.net/reader033/viewer/2022051415/56649d005503460f949d1957/html5/thumbnails/10.jpg)
AREA OF A PARALLELOGRAM
Since the area of the rectangle and parallelogram are the same, just rearranged, what is the formula for the
area of this parallelogram?
h
b
bhA hbA bhA 2
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Congratulations!!!
You Answered Correctly.
Click to continue.
![Page 12: Which of the following areas are you trying to find? ParallelogramTriangleTrapezoid AREAS OF POLYGONS](https://reader033.vdocuments.net/reader033/viewer/2022051415/56649d005503460f949d1957/html5/thumbnails/12.jpg)
The next slide will take you into discovering the
area of a triangle.
Do you wish to continue?
Yes No
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AREA OF A TRIANGLE
Hello. You will now be discovering the formula for area of a triangle.h
bClick to Continue
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AREA OF A TRIANGLE
Let’s divide the triangle so that we divide the
height in two.
b
?
?
Click to Continue
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AREA OF A TRIANGLE
Now take the top and rotate…
b
?
?
Click to Continue
Remember, we divided the height into two equal
parts.
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AREA OF A TRIANGLE
rotate…
?
?
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AREA OF A TRIANGLE
?
?
b
rotate…
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AREA OF A TRIANGLE
?
?
b
rotate…
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AREA OF A TRIANGLE
?
?
b
rotate…
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AREA OF A TRIANGLE
?
?
b
rotate…
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AREA OF A TRIANGLE
??
b
…until you have a parallelogram.
How would you represent the height of this parallelogram?
h2 h21h
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AREA OF A TRIANGLE
??
b
b
?
?
Remember, you divided the height in two.
Click to Continue
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AREA OF A TRIANGLE
?
b
What is the area of this parallelogram?
bhA hbA 21 bhA 2
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Congratulations!!!
You Answered Correctly.
Click to continue.
![Page 25: Which of the following areas are you trying to find? ParallelogramTriangleTrapezoid AREAS OF POLYGONS](https://reader033.vdocuments.net/reader033/viewer/2022051415/56649d005503460f949d1957/html5/thumbnails/25.jpg)
AREA OF A TRIANGLE
The area of this triangle would be the same as the parallelogram. Therefore, the formula for the area of a triangle is… what?h
b
bhA hbA 21 bhA 2
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Congratulations!!!
You Answered Correctly.
Click to continue.
![Page 27: Which of the following areas are you trying to find? ParallelogramTriangleTrapezoid AREAS OF POLYGONS](https://reader033.vdocuments.net/reader033/viewer/2022051415/56649d005503460f949d1957/html5/thumbnails/27.jpg)
The next slide will take you into discovering the
area of a trapezoid.
Do you wish to continue?
Yes No
![Page 28: Which of the following areas are you trying to find? ParallelogramTriangleTrapezoid AREAS OF POLYGONS](https://reader033.vdocuments.net/reader033/viewer/2022051415/56649d005503460f949d1957/html5/thumbnails/28.jpg)
AREA OF A TRAPEZOID
Hi. Let’s derive the formula for the area for a trapezoid.
Click to Continue
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AREA OF A TRAPEZOID
Remember, there are two different bases on a trapezoid.
1b
2b
h
Click to Continue
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AREA OF A TRAPEZOID
1b
2b
?
?
First divide the trapezoid horizontally so the height is divided in two.
Click to Continue
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AREA OF A TRAPEZOID1b
2b
?
?
Remember, we divided the height in two. Now, rotate…
Click to Continue
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AREA OF A TRAPEZOID
1b
2b
?
?
rotate…
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AREA OF A TRAPEZOID
1b2b
? ?
…until, you have a parallelogram.
Click to Continue
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AREA OF A TRAPEZOID
1b2b
?
How would you represent the height of the parallelogram?
h h2 h21
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AREA OF A TRAPEZOID
1b
2b
?
? 1b2b
?
Remember, we divided the height in two.
Click to Continue
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AREA OF A TRAPEZOID
1b2b
?
How would you represent the base of the parallelogram?
)( 12 bb ))(( 21 bb )( 12 bb
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AREA OF A TRAPEZOID
1b
2b
?
? 1b2b
?
The new base is made by connecting the top and bottom bases.
Click to Continue
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AREA OF A TRAPEZOID
1b2b
?
How would you represent the area of this parallelogram?
)( 321 bhA )( 212
1 bbhA 2121 bhbA
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AREA OF A TRAPEZOID
It is improper to add subscripts.Try again.
Click to Continue
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AREA OF A TRAPEZOID
Reminder.In order to add before
multiplying you must use grouping symbols.
Click to Continue
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AREA OF A TRAPEZOID
The area of this trapezoid is the same as the parallelogram.
What is the formula for area of a trapezoid?
1b
2b
h
2121 bhbA )( 32
1 bhA )( 2121 bbhA
![Page 42: Which of the following areas are you trying to find? ParallelogramTriangleTrapezoid AREAS OF POLYGONS](https://reader033.vdocuments.net/reader033/viewer/2022051415/56649d005503460f949d1957/html5/thumbnails/42.jpg)
Congratulations!!!
You Answered Correctly.
Click to continue.
![Page 43: Which of the following areas are you trying to find? ParallelogramTriangleTrapezoid AREAS OF POLYGONS](https://reader033.vdocuments.net/reader033/viewer/2022051415/56649d005503460f949d1957/html5/thumbnails/43.jpg)
Sorry!!! Try again.
Click to continue.
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AREAS OF POLYGONS
Once you have finished with the handouts and tests you will have completed the unit on areas of parallelograms, triangles, and trapezoids.
Have a good day.
Click to Continue