Here is the slide-by-slide Visualizing the Maximim Area of a 4-Sided Rectangular Enclosure Keynote presentation I used to create the YouTube animation explaining this concept.

1. What is the maximum 4-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?
Perimeter =
100 m
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3. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
5 m
Perimeter =
100 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
5 m 5 m
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5. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
45 m
5 m 5 m
45 m
www.tapintoteenminds.com @MathletePearce

6. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
45 m
5 m 5 m
45 m
Area =
lw
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7. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
45 m
5 m 5 m
45 m
Area = ( 4 5 m )w
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8. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
45 m
5 m 5 m
45 m
Area = ( 4 5 m ) ( 5 m )
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9. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
45 m
5 m 5 m
45 m
Area = ( 4 5 m ) ( 5 m )
= 225 m2
www.tapintoteenminds.com @MathletePearce

10. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
45 m
5 m 5 m
45 m
Area =
( 4 5 m ) ( 5 m )
= 225 m2
Width Area
www.tapintoteenminds.com @MathletePearce

11. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
45 m
5 m 5 m
45 m
Area =
( 4 5 m ) ( 5 m )
= 225 m2
Width Area
5 m
www.tapintoteenminds.com @MathletePearce

12. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
45 m
5 m 5 m
45 m
Area =
( 4 5 m ) ( 5 m )
= 225 m2
Width Area
5 m
225 m2
www.tapintoteenminds.com @MathletePearce

13. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
www.tapintoteenminds.com @MathletePearce

14. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
100 m
www.tapintoteenminds.com @MathletePearce

15. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
www.tapintoteenminds.com @MathletePearce

16. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
15 m 15 m
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17. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
15 m
35 m
35 m
15 m
www.tapintoteenminds.com @MathletePearce

18. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
15 m
Perimeter = 100 m
35 m
35 m
15 m
Area = lw
www.tapintoteenminds.com @MathletePearce

19. 15 m
What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
35 m
35 m
Perimeter = 100 m
15 m
Area = ( )w
35 m
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20. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
( 3 5 m
)( 1 5 m )
15 m
35 35 m
15 m
Area =
35 m
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21. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
( 3 5 m
)( 1 5 m )
35 m
35 m
15 m
35 15 m
Area =
= 525 m2
www.tapintoteenminds.com @MathletePearce

22. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
35 m
Perimeter = 100 m
15 m
( 3 5 m
)( 1 5 m ) 35 m
525 m2
15 m
35 Area =
Width Area
5 m 225 m2
= www.tapintoteenminds.com @MathletePearce

23. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
35 m
Perimeter = 100 m
15 m
( 3 5 m
)( 1 5 m ) 35 m
525 m2
15 m
35 Area =
Width Area
5 m 225 m2
= www.tapintoteenminds.com @MathletePearce

24. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
15 m
( 3 5 m
)( 1 5 m ) Area =
= 525 m2
15 m
35 35 m
Width Area
5 m 225 m2
35 m
15 m
www.tapintoteenminds.com @MathletePearce

25. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
15 m
( 3 5 m
)( 1 5 m ) Area =
= 525 m2
15 m
35 35 m
Width Area
5 m 225 m2
35 m
15 m
525 m2
www.tapintoteenminds.com @MathletePearce

26. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
15 m
15 m
Width Area
5 m 225 m2
15 m
35 m
( 3 5 m
)( ) 35 m
15 m
35 Area =
= 525 m2
525 m2
www.tapintoteenminds.com @MathletePearce

27. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
100 m
www.tapintoteenminds.com @MathletePearce

28. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
25 m 25 m
Perimeter = 100 m
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29. 25 m
25 m
25 m
25 m
What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
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30. 25 m
25 m
25 m
25 m
What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
Area = lw
www.tapintoteenminds.com @MathletePearce

31. 25 m
25 m
25 m
25 m
What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
Area = ( 2 5 m
)w
25 www.tapintoteenminds.com @MathletePearce

32. 25 m
25 m
25 m
25 m
What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
Area = ( 2 5 m )( 2 5 m )
www.tapintoteenminds.com @MathletePearce

33. 25 m
25 m
25 m
25 m
What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
Area = ( 2 5 m )( 2 5 m )
= 625 m2
www.tapintoteenminds.com @MathletePearce

34. Width Area
5 m 225 m2
15 m
25 m
25 m
25 m
25 m
What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
Area = ( 2 5 m )( 2 5 m )
= 625 m2
525 m2
www.tapintoteenminds.com @MathletePearce

35. 25 m
25 m
25 m
25 m
What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
Area = ( 2 5 m )( 2 5 m )
= 625 m2
Width Area
5 m 225 m2
15 m 525 m2
25 m
www.tapintoteenminds.com @MathletePearce

36. 25 m
25 m
25 m
25 m
What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
Area = ( 2 5 m )( 2 5 m )
= 625 m2
Width Area
5 m 225 m2
15 m 525 m2
625 m2
25 m
www.tapintoteenminds.com @MathletePearce

37. 25 m
25 m
25 m
25 m
What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter = 100 m
Area = ( 2 5 m )( 2 5 m )
= 625 m2
Width Area
5 m 225 m2
15 m 525 m2
625 m2
25 m
www.tapintoteenminds.com @MathletePearce

38. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
100 m
www.tapintoteenminds.com @MathletePearce

39. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter =
15 m
Area = ( 15 1 5 m
)( 3 5 m
) 35 m 35 m
100 m
= 525 m2
15 m
35 www.tapintoteenminds.com @MathletePearce

40. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter =
15 m
Area = ( 15 1 5 m
)( 3 5 m
) 35 m 35 m
100 m
= 525 m2
Width Area
5 m 225 m2
15 m 525 m2
25 m 625 m2
15 m
35 35 m
www.tapintoteenminds.com @MathletePearce

41. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter =
15 m
Area = ( 15 1 5 m
)( 3 5 m
) 35 m 35 m
100 m
= 525 m2
Width Area
5 m 225 m2
15 m 525 m2
25 m 625 m2
15 m
35 35 m
525 m2
www.tapintoteenminds.com @MathletePearce

42. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Perimeter =
15 m
Area = ( 15 1 5 m
)( 3 5 m
) 35 m 35 m
100 m
= 525 m2
Width Area
5 m 225 m2
15 m 525 m2
25 m 625 m2
15 m
35 35 m
525 m2
www.tapintoteenminds.com @MathletePearce

43. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
100 m
Width Area
5 m 225 m2
15 m 525 m2
25 m 625 m2
Perimeter =
35 m 525 m2
www.tapintoteenminds.com @MathletePearce

44. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
100 m
Width Area
5 m 225 m2
15 m 525 m2
25 m 625 m2
Perimeter =
35 m 525 m2
45 m 225 m2
www.tapintoteenminds.com @MathletePearce

45. Perimeter =
5 m
Area = ( 4 5 m ) 45 m 45 m
( 5 m
)
= 100 m
Width Area
5 m 225 m2
15 m 525 m2
25 m 625 m2
5 m
35 m 225 m2
525 m2
45 m 225 m2
www.tapintoteenminds.com @MathletePearce

46. Perimeter =
5 m
Area = ( 4 5 m ) 45 m 45 m
( 5 m
)
= 100 m
Width Area
5 m 225 m2
15 m 525 m2
25 m 625 m2
5 m
35 m 225 m2
525 m2
45 m 225 m2
www.tapintoteenminds.com @MathletePearce

47. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
Width Area
5 m 225 m2
15 m 525 m2
25 m 625 m2
35 m 525 m2
45 m 225 m2
100 m
Perimeter =
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48. What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
25 m
100 m
Perimeter =
Width Area
5 m 225 m2
15 m 525 m2 25 m 25 m
25 m 625 m2
25 m
35 m 525 m2
45 m 225 m2
www.tapintoteenminds.com @MathletePearce

49. A SQUARE WILL
ALWAYS MAXIMIZE
AREA OF 4-SIDED
ENCLOSURES
What is the maximum 4-sided rectangular
area we can enclose given 100 m of rope?
25 m
100 m
Perimeter =
Width Area
5 m 225 m
15 m 525 m 25 m 25 m
25 m 625 m
25 m
35 m 525 m
45 m 225 m
www.tapintoteenminds.com @MathletePearce