This show is intended for students who were absent from class on the day of the task.

AREA I: MAXIMIZING

AREA WITH A FIXED

PERIMETERThis show is intended for students

who were absent from class on the day of the task.

MAIN MENUClick on a question for assistance.

Question #1

Question #5Question

#2Question

#6Question #3

Question #7aQuestion

#4Question

#7bExit Presentation

READ THE TASK. THEN ANSWER THE FOLLOWING QUESTION.

Which rectangle below has a perimeter of 20 units? Click on the answer of your choice.

CORRECT! GREAT JOB!Now complete problem #1 on your handout by sketching several rectangles with a perimeter of 20 units.

Click here to continue to #2

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INCORRECT – YOU HAVE CONFUSED AREA WITH PERIMETER!

You have confused area with perimeter. In order to find the perimeter of a rectangle, do you multiply the base by the height, OR do you add all of the side lengths?

Multiply the base by the height

Add all of the side lengths

INCORRECT – YOU HAVE CONFUSED AREA WITH PERIMETER!

In order to find the perimeter of a rectangle, you add all of the side lengths. Click anywhere on slide to reveal the perimeter of each rectangle.

195

4𝑃=1+9+1+9

units𝑃=4+5+4+5

units

Click to continue

to #2

When you are ready, complete sketches for

#1.

sCORRECT! GREAT JOB!Now complete problem #1 on your handout by sketching several rectangles with a perimeter of 20 units.

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QESTION 2: Look at each of your sketches of a rectangle with a perimeter of 20 units. What do you notice aboutthe relationship between the base and height?

Click here for Hint

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QESTION 2: HINT

Try adding, subtracting, multiplying and dividing each base and height. Do you notice a pattern using any of these operations?

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QUESTION 3-TABLENote: You do not need to complete the entire table in order to be able to make a graph. If you are unable to notice anything about the area in the table or graph, you may want to add more data to your table.

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QUESTION 4-GRAPHWhich diagram below looks like your graph?

WATCH!Look at the labels on the graph. Notice that you are graphing how the base is related to the AREA.

You are NOT graphing how the base is related to the HEIGHT.

Redo your graph. Then click continue.

Continue

WHAT HAPPENS AS THE BASE INCREASES?As your base increases, what happens to your area? Yes, it increases.

Will the area continue to increase when the base gets longer than 5 ft? How do you know?

If you are not sure, calculate the areaof rectangles when the base is longerthan 5 ft. Enter this data into your table and plot these points. Then click continue.

Continue

WHAT HAPPENS AS THE BASE DECREASES?As your base decreases, what happens to your area? Yes, it increases.

Will the area continue to increase when the base gets shorter than 5 ft? How do you know?

If you are not sure, calculate the areaof rectangles when the base is shorterthan 5 ft. Enter this data into your table and plot these points. Then click continue.

Continue

EXCELLENT WORK!Your graph is complete. Why does the area increase and then decrease? Is there a logical reason for this?

After you have considered the question above, continue to question #5 or return to MAIN MENU.

MAIN MENU


TRY QUESTION 4 AGAINWhich diagram below looks like your graph?

QUESTION 5What dimensions (base and height) will enclose the greatest area using 20 ft of fencing?

4 ft by 6 ft

5 ft by 5 ft

INCORRECTIs a square a rectangle?

YES

NO

CORRECT!A square is a rectangle.

On your graph, when the base is 4 ft, the area is 24 sq ft. When the base is 6 ft, the area is 24 sq ft. What happens in between these two points? Is the area larger or smaller than 24 sq ft?

After answering this question, click below to return to Question #5.

Return to Question #5

INCORRECTA rectangle is an equiangular parallelogram.

In other words it has two pairs of parallel sides and all right angles.

Does a square have two pairs of parallel sides and all right angles? If so, then a square is a rectangle.


CORRECT! EXCELLENT WORK.Continue to question #6 or go back to the MAIN MENU.

MAIN MENU


QUESTION 6What kind of rectangle is your result from #5? If your rectangle is not a particular type, you may want to go back to question #5 before continuing.

Click to Continue


QUESTION 6 CONTINUED…Do you think that would be the result for any fixed perimeter? In other words, if I gave you a new fixed perimeter (for example: 50 ft), would this same shape give you the maximum area?

NO

YES

CORRECT!When you look at your graph, you will notice that the area increases and then decreases. This happens because the base and height switch. This will always happen when calculating the area of a rectangle, so there will always be a maximum area when the side lengths are the same. Therefore, a square will always give you the maximum area when given a fixed perimeter.

MAIN MENU

Click here to continue to #7a

INCORRECTWhen you look at your graph, you will notice that the area increases and then decreases. This happens because the base and height switch. This will always happen when calculating the area of a rectangle, so there will always be a maximum area when the side lengths are the same. Therefore, a square will always give you the maximum area when given a fixed perimeter.

MAIN MENU

b=4’h=6’

b=6’h=4’

Maximum(dimensions are the

same length)

QUESTION 7AA gardener has 68 ft of fencing. What dimensions would enclose the greatest area?

17 ft by 17 ft

16 ft by 18 ft

CORRECT!Excellent work. Now calculate the maximum area in part b. Click MAIN MENU below.

MAIN MENU

Click here to continue to #7b

INCORRECTWhat kind of rectangle will give you the maximum area if you have a fixed perimeter?

Click below to go back to Question #6. Then try this problem again.


QUESTION 7BA gardener has 68 ft of fencing. How much area would your dimensions from #7a enclose?

289 sq ft

288 sq ft

CORRECT!Excellent work. Click MAIN MENU below if you have more questions or exit the presentation if you are finished completing the task.

MAIN MENU

Exit Presentation

INCORRECTWhat kind of rectangle will give you the maximum area if you have a fixed perimeter?

Click below to go back to Question #6. Then try this problem again.


This show is intended for students who were absent from class on the day of the task.

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