Doubling the Sides of a Polygon

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Doubling the Sides of a Polygon

• Its twice as much fun as multiplying by 2.

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Lets begin with a simple square that measures 5
cm on each side.
5 cm
5 cm
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What is the area of this square?
5 cm
5 cm
4
Thats right! Its 25 square cm. because 5 x 5
25.
5 cm
5 cm
5
Now lets stretch this square by a factor of 2.
5 cm
5 cm
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Now lets stretch this square by a factor of 2.
10 cm
10 cm
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The stretched square has 4 original squares
inside of it.
10 cm
10 cm
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The original area of 25 sq. cm. stretches to 100
sq. cm.
10 cm
10 cm
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This is an increase in area by a factor of 4.
10 cm
10 cm
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Now lets try stretching a rectangle.
5 m
2 m
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This rectangle has an area of 10 square meters.
5 m
2 m
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Now lets stretch this rectangle by a factor of 2.
5 m
2 m
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Now lets stretch this rectangle by a factor of 2.
10 m
4 m
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This stretched rectangle is made of 4 original
rectangles.
10 m
4 m
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This rectangle has an area of 40 square meters.
10 m
4 m
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The original area of 10 square meters stretches
to 40 square meters.
10 m
4 m
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This is an increase in area by a factor of 4.
10 m
4 m
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Now lets try stretching a triangle.
5 cm
3 cm
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Lets stretch this triangle by a factor of 2.
5 cm
3 cm
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Lets stretch this triangle by a factor of 2.
10 cm
6 cm
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You can fit 4 of the original triangles inside of
the stretched triangle.
10 cm
6 cm
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Take any quadrilateral, double the length, double
the width, and the area will quadruple.
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Take any quadrilateral, double the length, double
the width, and the area will quadruple.
5 cm
6 cm
Area 5 x 6 30 cm2
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Area 10 x 12 120 cm2
Take any quadrilateral, double the length, double
the width, and the area will quadruple.
10 cm
12 cm
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Take any quadrilateral, double the length, double
the width, and the area will quadruple.
1
2
10 cm
3
4
12 cm
Area 5 x 6 30 cm2 Area 10 x 12 120 cm2
x 4
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In fact, if you stretch any polygon by a factor
of 2, then the area will quadruple.
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In fact, if you stretch any polygon by a factor
of 2, then the area will quadruple.
3 cm
Area 34 cm2
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In fact, if you stretch any polygon by a factor
of 2, then the area will quadruple.
6 cm
Area 136 cm2
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In fact, if you stretch any polygon by a factor
of 2, then the area will quadruple.
3 cm
Area 34 cm2
x 4
6 cm
Area 136 cm2
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Practice Time!
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1) Imagine that you doubled the length and
doubled the width of this square. What would be
the new area?
4 cm
4 cm
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1) Imagine that you doubled the length and
doubled the width of this square. What would be
the new area?
8 cm
Area 8 x 8 64 cm2
8 cm
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2) Study the small and large triangles below
12 cm
6 cm
3 cm
6 cm
How many little triangles would fit inside this
shape?
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2) Study the small and large triangles below
4 small triangles fit in one large triangle.
12 cm
6 cm
3 cm
6 cm
How many little triangles would fit inside this
shape?
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2) Study the small and large triangles below
12 cm
6 cm
16 small triangles fit in 4 large triangles.
3 cm
6 cm
How many little triangles would fit inside this
shape?
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3) Imagine that you were making a square blanket
out of 16 small squares.
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3) Imagine that you were making a square blanket
out of 16 small squares.
Then you decide to make the blanket larger by
doubling the length and doubling the width. How
many additional squares are required to do this?
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3) Imagine that you were making a square blanket
out of 16 small squares.
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3) Imagine that you were making a square blanket
out of 16 small squares.
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3) Imagine that you were making a square blanket
out of 16 small squares.
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3) Imagine that you were making a square blanket
out of 16 small squares.
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3) Imagine that you were making a square blanket
out of 16 small squares.
16 x 3 48 additional squares
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4) Kathys grandmother has a garden that is the
shape of a regular hexagon. Each side is 4 ft.
long.
4 ft
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4) She would like to make the garden bigger so
that each side will be 8 ft. long.
4 ft
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4) How much greater will the area of the new
garden be than the area of the old garden?
4 ft
8 ft
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4) How much greater will the area of the new
garden be than the area of the old garden?
x 4
4 ft
The area will be 4 times greater.
8 ft
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5) Look at the square below.
4
4
Which of the following squares has an area that
is 4 times greater than this square?
A) 6 by 6 square
B) 8 by 8 square
C) 16 by 16 square
D) 20 by 20 square
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5) Look at the square below.
Area 4 x 4 16
4
4
x 4
Area 8 x 8 64
A) 6 by 6 square
B) 8 by 8 square
C) 16 by 16 square
D) 20 by 20 square
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6) A square has an area 36. What is the area of
a square whose length and width are half the size
of this square?
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6) A square has an area 36. What is the area of
a square whose length and width are half the size
of this square?
Area 36
6
6
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6) A square has an area 36. What is the area of
a square whose length and width are half the size
of this square?
Area 36
6
Area 9
3
3
6
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THE END!