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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.
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100 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
Perimeter =
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
100 m
5 m
Perimeter =
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
100 m
5 m 5 m
Perimeter =
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
100 m
45 m
45 m5 m 5 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
Perimeter = 100 m
45 m
45 m5 m 5 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
Area =
5 m 5 m45 m
45 m
lw
Perimeter = 100 m
45 m
45 m5 m 5 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
Area = ( )w45 m45 m
5 m 5 m
Perimeter = 100 m
45 m
45 m5 m 5 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
Area = ( ) ( )45 m45 m 5 m5 m
Perimeter = 100 m
45 m
45 m5 m 5 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
Area = ( ) ( )45 m45 m 5 m5 m
Perimeter = 100 m
= 225 m2225 m2
45 m
45 m5 m 5 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
Area == 225 m2
( ) ( )45 m45 m 5 m5 m
Width AreaPerimeter = 100 m
225 m2
5 m 5 m
45 m
45 m5 m 5 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
Area == 225 m2
( ) ( )45 m45 m 5 m
5 m
Width AreaPerimeter = 100 m
5 m
225 m2
5 m
225 m2
45 m
45 m5 m 5 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
Area == 225 m2
( ) ( )45 m45 m 5 m
Width AreaPerimeter = 100 m
5 m
225 m2
225 m2
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
Perimeter = 100 m
100 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
35 m
35 m
Perimeter = 100 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
35 m
35 m
15 m 15 m
Perimeter = 100 m
35 m
35 m
15 m15 m 15 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
35 m
35 m
15 m
Perimeter = 100 m
35 m
35 m
15 m15 m 15 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
35 m
35 m
15 m
Area = lw
Perimeter = 100 m
35 m
35 m
15 m15 m 15 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
35 m
35 m
15 m
Area = ( )w
Perimeter = 100 m
35 m35 m
15 m( )35 m ( )15 m
35 m
15 m
35 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
35 m
15 m
Area =
Perimeter = 100 m
35 m
525 m2
15 m( )35 m ( )15 m
35 m
15 m
35 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
35 m
15 m
Area =
Perimeter = 100 m
= 525 m2
35 m
525 m2
15 m( )35 m ( )15 m 35 m
15 m
35 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
35 m
15 m
Area =
Width Area
5 m 225 m2
Perimeter = 100 m
= 525 m2
35 m
525 m2
15 m15 m
15 m15 m( )35 m ( )15 m 35 m
15 m
35 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
35 m
15 m
Area =
Width Area
5 m 225 m2
Perimeter = 100 m
= 525 m2
35 m
15 m15 m
= 525 m2525 m2
15 m( )35 m ( )15 m 35 m
15 m
35 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
35 m
15 m
Area =
Width Area
5 m 225 m2
Perimeter = 100 m
35 m15 m
525 m2
15 m15 m
= 525 m2525 m2
15 m( )35 m ( )15 m 35 m
15 m
35 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
35 m
15 m
Area =
Width Area
5 m 225 m2
Perimeter = 100 m
35 m15 m 525 m2
15 m
525 m2
15 m
( )35 m ( ) 35 m
15 m
35 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
35 m
15 m
Area =
Width Area
5 m 225 m2
Perimeter = 100 m
= 525 m2
35 m525 m2
100 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
25 m 25 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
Perimeter = 100 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?
@MathletePearcewww.tapintoteenminds.com
Perimeter = 100 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?
@MathletePearcewww.tapintoteenminds.com
Perimeter = 100 m
Area = lw
25 m
25 m
25 m
25 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?
@MathletePearcewww.tapintoteenminds.com
Perimeter = 100 m
Area = ( )w25 m25 m
25 m25 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?
@MathletePearcewww.tapintoteenminds.com
Perimeter = 100 m
Area = ( )( )25 m 25 m25 m 25 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?
@MathletePearcewww.tapintoteenminds.com
Perimeter = 100 m
Area = ( )( )25 m 25 m25 m 25 m
= 625 m2625 m2625 m2
25 m
25 m
25 m
25 m
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?
@MathletePearcewww.tapintoteenminds.com
Perimeter = 100 m
Area = ( )( )25 m 25 m25 m 25 m
= 625 m2625 m2625 m2
25 m
25 m
25 m
25 m
Width Area
5 m 225 m2
525 m2
25 m
25 m
25 m
25 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
Perimeter = 100 m
Area = ( )( )25 m 25 m25 m
= 625 m2625 m2625 m2
25 m
25 m
25 m
25 m
Width Area
5 m 225 m2
15 m 525 m2
25 m
25 m
25 m
25 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
Perimeter = 100 m
Area = ( )( )25 m 25 m25 m25 m
= 625 m2625 m2
625 m2
25 m
25 m
25 m
25 m
Width Area
5 m 225 m2
15 m 525 m2
25 m
25 m
25 m
25 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
Perimeter = 100 m
Area = ( )( )25 m 25 m25 m25 m
= 625 m2625 m2
625 m2
25 m
25 m
25 m
25 m
Width Area
5 m 225 m2
15 m 525 m2
100 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
= 525 m2
15 m
100 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
Perimeter =
Area = ( )( )15 m 35 m 35 m 35 m
15 m
15 m
35 m
525 m2
= 525 m2
15 m
100 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
25 m 625 m225 m25 m
Width Area
5 m 225 m2
15 m 525 m2
Perimeter =
Area = ( )( )15 m 35 m 35 m 35 m
15 m
15 m
35 m
35 m525 m2
= 525 m2
15 m
100 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
25 m 625 m225 m25 m
Width Area
5 m 225 m2
15 m 525 m2
Perimeter =
Area = ( )( )15 m 35 m 35 m 35 m
15 m
15 m
35 m
35 m525 m2
525 m2
= 525 m2
15 m
100 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
25 m 625 m225 m25 m
Width Area
5 m 225 m2
15 m 525 m2
Perimeter =
Area = ( )( )15 m 35 m 35 m 35 m
15 m
15 m
35 m
35 m525 m2
525 m2
100 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
25 m 625 m225 m25 m
Width Area
5 m 225 m2
15 m 525 m2
Perimeter =
35 m 525 m2
100 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
@MathletePearcewww.tapintoteenminds.com
25 m 625 m225 m25 m
Width Area
5 m 225 m2
15 m 525 m2
Perimeter =
35 m 525 m2
45 m 225 m2
( )
= 225 m2
5 m
100 m
@MathletePearcewww.tapintoteenminds.com
25 m 625 m225 m25 m
Width Area
5 m 225 m2
15 m 525 m2
Perimeter =
Area = ( )45 m 45 m 45 m
5 m
5 m
35 m 225 m2525 m2
45 m 225 m2
( )
= 225 m2
5 m
100 m
@MathletePearcewww.tapintoteenminds.com
25 m 625 m2
Width Area
5 m 225 m2
15 m 525 m2
Perimeter =
Area = ( )45 m 45 m 45 m
5 m
5 m
35 m 225 m2525 m2
45 m 225 m2
@MathletePearcewww.tapintoteenminds.com
25 m 625 m2
Width Area
5 m 225 m2
15 m 525 m2
35 m 525 m2
45 m 225 m2
100 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
Perimeter =
@MathletePearcewww.tapintoteenminds.com
25 m 625 m2
Width Area
5 m 225 m2
15 m 525 m2 25 m 25 m
25 m
25 m35 m 525 m2
45 m 225 m2
100 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
Perimeter =
@MathletePearcewww.tapintoteenminds.com
25 m 625 m
Width Area
5 m 225 m15 m 525 m 25 m 25 m
25 m
25 m35 m 525 m45 m 225 m
100 m
What is the maximum 4-sided rectangular area we can enclose given 100 m of rope?
Perimeter =
A SQUARE WILL
ALWAYS MAXIMIZE
AREA OF 4-SIDED
ENCLOSURES
