Perimeter
Chapter 12
Measurement
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The perimeter
perimeter,, P, of a polygon is the
distance around the polygon – or the sum of
the lengths of each side of the polygon.
Perimeter is a linear measurement.
measurement
Section 12.2
Measuring the Perimeter
and Area of Polygons
Common Formulas for Perimeter
Area
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A Question
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You have $100 to spend on fencing that costs
$2.50 per foot. What is the largest area you
could fence in?
The area,
area, A, of a polygon is the number of square
units the polygon covers.
Activity
Relating Perimeter and Area
(Rectangles and Squares)
1
Comparing Perimeters and Areas of
Similar Polygons
Investigation
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Draw a rectangle whose length is 6 cm and
whose width is 4 cm.
Draw a second rectangle whose length is 9
cm and whose width is 6 cm.
What is the relationship between these two
quadrilaterals?
Find the perimeter and area of each.
Compare the ratios between corresponding
sides, perimeters, and areas. What do you
notice?
Activity:
Connecting Area of
Parallelograms, Triangles, and Trapezoids
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The ratio of the perimeters is the same as
the ratio of any two corresponding sides
(scale factor).
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If the scale factor of two similar polygons is
a : b, then the ratio between their areas is
a² : b².
Activity continued:
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What would be the formula for finding the area of a
parallelogram?
On a piece of grid paper, draw a rectangle with a base
of 6 cm and a height of 4cm. Find the area.
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Draw another parallelogram. Draw a diagonal of the
parallelogram.
What is the general formula for finding the area of a
rectangle? Why?
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What figures are formed? How are the areas of each
related? What would be the formula for finding the
area of a triangle?
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Draw a trapezoid. Draw a diagonal of the trapezoid.
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How can we develop a formula for finding the area of
the trapezoid by using the area of the two triangles
and the distributive property?
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Use a colored pencil to rearrange the rectangle to
make a parallelogram. Identify the base and height.
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How are the base and height related to the length and
width of the rectangle? How are the areas related?
Area Formulas
Area Formulas
2
Examples
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Textbook: Page 752.
1.))
2.)
3.)
4.)
#10
#12
#18
#20
Circumference of Circles
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The circumference
circumference,, C, of a circle is the
distance around the circle.
How is circumference similar to perimeter?
Different?
Diff
?
Developing a Formula for Circumference
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Discovering Pi
Activity: Discovering Pi
Bring in several circular objects and have
students use a piece of string and a ruler to
determine the circumference and diameter
of each circle. Then, they will determine the
ratio between the circumference and the
diameter, П !
Object
Circumference
Diameter
Circumference
Diameter
Circumference of a Circle Formula
Developing Area Formula for a Circle
П = Circumference ≈ 3.14 or 22
Diameter
7
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Draw a circle and cut it into 8 equal parts.
Arrange the parts into the general shape of a
parallelogram.
H can this
How
hi b
be used
d to arrive
i at the
h area ffor
a circle?
3
Area of Circle Formula
Examples
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Textbook: Page 752.
1.)) #24
2.) #34
3.) #62
4.) #63
4