Area and Perimeter of Rectangles

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Area and Perimeter of Rectangles

• For this activity,you will need 40 square tiles.

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1) Using your squares, construct a rectangle that
has an area of 12.
3
There are several possible solutions to this
problem.
4
3
4
There are several possible solutions to this
problem.
2
6
5
There are several possible solutions to this
problem.
1
12
6
Fill in the blank.The numbers 3, 4, 2, 6, 1, and
12 are __________ of the number 12.
2
4
6
3
1
12
7
Fill in the blank.The numbers 3, 4, 2, 6, 1, and
12 are factors of the number 12.
2
4
6
3
1
12
8
Does a 3 by 5 have the same area as a 5 by 3?
5
3
3
5
9
This is the same as asking, Is 5 x 3 the same as
3 x 5?
5
3
3
5
10
What property says that these two shapes do
indeed cover the same area?
5
3
3
5
11
What property says that these two shapes do
indeed cover the same area?
The Commutative Property
5
3
3
5
12
2) Using your squares, construct a rectangle that
has a perimeter of 12.
13
Again, there are several possible solutions.
5
1
1
5
14
Again, there are several possible solutions.
4
2
2
4
15
Again, there are several possible solutions.
3
3
3
3
16
Do you notice any pattern in the numbers that
make up all 3 solutions?
17
Do you notice any pattern in the numbers that
make up all 3 solutions?
18
Do you notice anything else?
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The sum of the length and width always equals 6.






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The perimeter that we were looking for was 12.
The length and width always sum to 6.
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What property says that you can find the
perimeter in the following manner?
Perimeter
(1x2) (5x2)
(2x2) (4x2)
(3x2) (3x2)
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What property says that you can find the
perimeter in the following manner?
The Distributive Property
Perimeter
(1x2) (5x2)
(2x2) (4x2)
(3x2) (3x2)
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3.) Using your squares, construct a rectangle
that has an area of 16, and a perimeter of 16.
24
There are several ways to get an area of 16.
8
4
2
4
1
16
25
There are several ways to get a perimeter of 16.
3
5
2
4
6
4
1
7
26
Which solution is common to both groups?
27
The 4 by 4 has an area of 16.
4
Area 4 x 4 16
4
28
The 4 by 4 has a perimeter of 16.
4
4
4
Perimeter 4 4 4 4 16
4
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4.) Using your squares, construct a rectangle
that has an area of 20 and a perimeter of 24.
30
The 2 by 10 has an area of 20.
2
Area 2 x 10 20
10
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The 2 by 10 has a perimeter of 24.
2
Perimeter 10 2 10 2 24
10
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5.) Using your squares, construct a rectangle
that has an area of 24 and a perimeter of 22.
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Heres the solution
8
3
Area 3 x 8 24 Perimeter 3 8 3 8 22
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6.) Construct a rectangle that has an area of 20
and a perimeter of 18.
35
Heres the solution
5
4
Area 4 x 5 20 Perimeter 4 5 4 5 18
36
7) Using your squares, construct a rectangle that
has an area of 40 and a perimeter of 28.
37
Heres the solution
10
4
Area 4 x 10 40 Perimeter 4 10 4 10
28
38
8.) Now, lets try solve the next problem without
the square tiles. What are the dimensions of a
rectangle that has an area of 60 and a perimeter
of 38?
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First, lets brainstorm the various ways to get a
product of 60.
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First, lets brainstorm the various ways to get a
product of 60.
1 x 60 2 x 30 3 x 20 4 x 15 5 x 12 6 x 10
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First, lets brainstorm the various ways to get a
product of 60.
1 x 60 2 x 30 3 x 20 4 x 15 5 x 12 6 x 10
One of these is our solution.
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Now we need to figure out which combination
results in a perimeter of 38.
1 x 60 2 x 30 3 x 20 4 x 15 5 x 12 6 x 10
One of these is our solution.
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Now we need to figure out which combination
results in a perimeter of 38.
1 60 1 60 2 30 2 30 3 20 3 20 4
15 4 15 5 12 5 12 6 10 6 10
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And the winner is
1 60 1 60 2 30 2 30 3 20 3 20 4
15 4 15 5 12 5 12 6 10 6 10
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And the winner is
1 60 1 60 2 30 2 30 3 20 3 20 4
15 4 15 38 5 12 5 12 6 10 6 10
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9.) The following rectangles all have an area of
16. Which rectangle minimizes the perimeter?
4
2
4
8
1
16
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4
Because this shape is a square and all 4 sides
are congruent, the perimeter will be minimized.
4
48
10.) The following rectangles all have an area of
16. Which rectangle maximizes perimeter?
4
2
4
8
1
16
49
Because this shape is so stretched out, the
perimeter will be maximized.
1
16
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10) Mr. Dunlap wants to build a garden and put a
fence around it. He has 18 yards of fencing.
How should he build the garden in order to
maximize the area?
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Because he has 18 yards of fence, this means that
the perimeter of the rectangle must be 18.
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Because he has 18 yards of fence, this means that
the perimeter of the rectangle must be 18.
Find all of the rectangles with a perimeter of 18.
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1
8
7
2
3
4
6
5
54
1
8
7
Which rectangle has the largest area?
2
3
4
6
5
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The 4 by 5 has the largest area (20).
4
5
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11) A rectangle has an area of 12. List all of
the possible perimeters for this rectangle.
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12
1
1
12
2
Perimeter 26
4
6
6
3
3
2
4
Perimeter 16
Perimeter 14
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12) A rectangle has an area of 16. List all of
the possible perimeters for this rectangle.
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1
1
not drawn to scale
2
16
Perimeter 34
4
8
8
4
4
4
2
Perimeter 16
Perimeter 20
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13) A rectangle has a perimeter of 10. List all
of the possible areas for this rectangle.
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2
1
3
4
Area 6
Area 4
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14) A rectangle has a perimeter of 16. List all
of the possible areas for this rectangle.
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4
Area 16
4
2
5
6
Area 12
1
3
7
Area 15
Area 7
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THE END!