Here is the slide-by-slide Visualizing the Maximim Area of a 3-Sided Rectangular Enclosure Keynote presentation I used to create the YouTube animation explaining this concept

1. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
100 m
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2. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
100 m
25 m
25 m
25 m
Perimeter =
25 m
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3. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter =
100 m
A SQUARE WILL
ALWAYS MAXIMIZE
AREA OF 4-SIDED
ENCLOSURES
25 m
25 m
25 m
25 m
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4. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
25 m
25 m 25 m
25 m
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5. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
25 m
25 m 25 m
25 m
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6. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
100 m
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25 m

7. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
90 m
5 m 5 m
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25 m
Area = (90 m)(5 m)

8. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
90 m
5 m 5 m
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25 m
Area = 450 m2

9. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
90 m
5 m 5 m
Width Area
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25 m
Area = 450 m2

10. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
90 m
5 m 5 m
Width Area
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25 m
Area = 450 m2
5 m 450 m2

11. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
Width Area
5 m 450 m2
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25 m

12. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
70 m
Width Area
5 m 450 m2
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25 m
15 m 15 m

13. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
70 m
Width Area
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25 m
Area = 1,050 m2
5 m 450 m2
15 m 15 m

14. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
70 m
Width Area
5 m 450 m2
15 m 1,050 m2 15 m 15 m
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25 m
Area = 1,050 m2

15. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
Width Area
5 m 450 m2
15 m 1,050 m2
www.tapintoteenminds.com @MathletePearce
25 m

16. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
25 m
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25 m
25 m 25 m
25 m

17. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
25 m
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25 m
25 m 25 m
25 m

18. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
25 m
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25 m
25 m 25 m
25 m

19. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
25 m
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25 m
25 m 25 m
25 m
3 sides

20. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
25 m
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25 m
25 m 25 m
25 m
3 sides
= 8.3 m

21. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
25 m
8.3 m
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25 m
25 m 25 m
25 m
3 sides
=
8.3 m 8.3 m 8.3 m

22. 25 m
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25 m
25 m 25 m
25 m
3 sides
=
8.3 m
8.3 m
8.3 m
8.3 m

23. 8.3 25 m
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25 m
25 m
25 m
25 m
3 sides
= 8.3 8.3 m 8.3

24. 33.3 m
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25 m
33.3 m 33.3 m
25 m
3 sides
= 8.3 m

25. 33.3 m
Area
33.3 m 33.3 m
=1,108.9 m2
Width Area
5 m 450 m2
15 m 1,050 m2
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26. 33.3 m
Width Area
5 m 450 m2
15 m 1,050 m2 33.3 m 33.3 m
Area
1,108.9 m2
1,108.9 m2 =
33.3 m
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27. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
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28. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
25 m
25 m 25 m
25 m
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29. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
25 m
25 m 25 m
25 m
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30. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
25 m 25 m
25 m 25 m
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31. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
25 m 25 m
Area
= (25 m)(25 m)
25 m 25 m
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32. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
25 m 25 m
Area
=
Area
25 m 25 m
(25 m)(25 m) =(25 m)(25 m)
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33. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
25 m 25 m
Area
= 625 m2
Area
= 625 m2
25 m 25 m
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34. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
25 m
25 m
Area
= 625 m2
25 m www.tapintoteenminds.com @MathletePearce

35. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
25 m
50 m
Area
25 m = 1,250 m2 www.tapintoteenminds.com @MathletePearce

36. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
Width Area
5 m 450 m2
15 m 1,050 m2
33.3 m 1,108.9 m2
50 m
Area
25 m 25 m
= 1,250 m2
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37. What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
Width Area
5 m 450 m2
15 m 1,050 m2
33.3 m 1,108.9 m2
50 m
Area
= 1,250 m2
25 m 25 m
25 m
1,250 m2
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38. MAKE A SQUARE AND
DOUBLE THE LENGTH
TO MAXIMIZE AREA OF
3-SIDED ENCLOSURES
What is the maximum 3-sided rectangular
area we can enclose given 100 m of rope?
Width Area
5 m 450 m
15 m 1,050 m
33.3 m 1,108.9 m
50 m
Area
= 1,250 m
25 m 25 m
25 m
1,250 m2
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39. What is the maximum 3-sided rectangular
area we can enclose given of rope?
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40. What is the maximum 3-sided rectangular
area we can enclose given 200 m
of rope?
50 m
50 m 50 m
50 m
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41. What is the maximum 3-sided rectangular
area we can enclose given 200 m
of rope?
50 m
50 m
50 m 50 m
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42. What is the maximum 3-sided rectangular
area we can enclose given of rope?
100 m
200 m
50 m Area = 5,000 m2 50 m
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