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
AREA OF A PARALLELOGRAM
Welcome. Today you’re going to discover the formula for area of a parallelogram.
h
b
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AREA OF A PARALLELOGRAM
To do this let’s cut the left triangle and…
h
b
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slide it…
AREA OF A PARALLELOGRAM
h
h b
Click to Continue
slide it…
AREA OF A PARALLELOGRAM
h
h
b
slide it…
AREA OF A PARALLELOGRAM
h
h
b
slide it…
AREA OF A PARALLELOGRAM
h
hb
…thus, changing it to a rectangle.
What is the area of the rectangle?
AREA OF PARALLELOGRAM
h
b
bhA hbA bhA 2
Congratulations!!!
You Answered Correctly.
Click to continue.
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
Congratulations!!!
You Answered Correctly.
Click to continue.
The next slide will take you into discovering the
area of a triangle.
Do you wish to continue?
Yes No
AREA OF A TRIANGLE
Hello. You will now be discovering the formula for area of a triangle.h
bClick to Continue
AREA OF A TRIANGLE
Let’s divide the triangle so that we divide the
height in two.
b
?
?
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AREA OF A TRIANGLE
Now take the top and rotate…
b
?
?
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Remember, we divided the height into two equal
parts.
AREA OF A TRIANGLE
rotate…
?
?
AREA OF A TRIANGLE
?
?
b
rotate…
AREA OF A TRIANGLE
?
?
b
rotate…
AREA OF A TRIANGLE
?
?
b
rotate…
AREA OF A TRIANGLE
?
?
b
rotate…
AREA OF A TRIANGLE
??
b
…until you have a parallelogram.
How would you represent the height of this parallelogram?
h2 h21h
AREA OF A TRIANGLE
??
b
b
?
?
Remember, you divided the height in two.
Click to Continue
AREA OF A TRIANGLE
?
b
What is the area of this parallelogram?
bhA hbA 21 bhA 2
Congratulations!!!
You Answered Correctly.
Click to continue.
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
Congratulations!!!
You Answered Correctly.
Click to continue.
The next slide will take you into discovering the
area of a trapezoid.
Do you wish to continue?
Yes No
AREA OF A TRAPEZOID
Hi. Let’s derive the formula for the area for a trapezoid.
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AREA OF A TRAPEZOID
Remember, there are two different bases on a trapezoid.
1b
2b
h
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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
AREA OF A TRAPEZOID1b
2b
?
?
Remember, we divided the height in two. Now, rotate…
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AREA OF A TRAPEZOID
1b
2b
?
?
rotate…
AREA OF A TRAPEZOID
1b2b
? ?
…until, you have a parallelogram.
Click to Continue
AREA OF A TRAPEZOID
1b2b
?
How would you represent the height of the parallelogram?
h h2 h21
AREA OF A TRAPEZOID
1b
2b
?
? 1b2b
?
Remember, we divided the height in two.
Click to Continue
AREA OF A TRAPEZOID
1b2b
?
How would you represent the base of the parallelogram?
)( 12 bb ))(( 21 bb )( 12 bb
AREA OF A TRAPEZOID
1b
2b
?
? 1b2b
?
The new base is made by connecting the top and bottom bases.
Click to Continue
AREA OF A TRAPEZOID
1b2b
?
How would you represent the area of this parallelogram?
)( 321 bhA )( 212
1 bbhA 2121 bhbA
AREA OF A TRAPEZOID
It is improper to add subscripts.Try again.
Click to Continue
AREA OF A TRAPEZOID
Reminder.In order to add before
multiplying you must use grouping symbols.
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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
Congratulations!!!
You Answered Correctly.
Click to continue.
Sorry!!! Try again.
Click to continue.
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.
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