Geometry: Perimeter and Area€¦ · Geometry: Perimeter and Area Melissa Kramer Laingsburg High...
Transcript of Geometry: Perimeter and Area€¦ · Geometry: Perimeter and Area Melissa Kramer Laingsburg High...
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Geometry:
Perimeter
and Area Melissa Kramer
Laingsburg High School
Laingsburg, Michigan
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A polygon is a
closed plane
figure formed by
three or more
segments
Each segment intersects
exactly two others at their
endpoints.
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Names of Polygons
# of Sides Name
3 Triangle
4 Quadrilateral
5
6
7 Heptagon
8
9 Nonagon
10
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Names of Polygons
# of Sides Name
3 Triangle
4 Quadrilateral
5 Pentagon
6
7 Heptagon
8
9 Nonagon
10
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Names of Polygons
# of Sides Name
3 Triangle
4 Quadrilateral
5 Pentagon
6 Hexagon
7 Heptagon
8
9 Nonagon
10
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Names of Polygons
# of Sides Name
3 Triangle
4 Quadrilateral
5 Pentagon
6 Hexagon
7 Heptagon
8 Octagon
9 Nonagon
10
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Names of Polygons
# of Sides Name
3 Triangle
4 Quadrilateral
5 Pentagon
6 Hexagon
7 Heptagon
8 Octagon
9 Nonagon
10 Decagon
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Two Types of Polygons
Concave: Has at least one corner
“pushed in” toward the center
Convex: All corners point away from the
center
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Essential Understanding: Perimeter and area are two DIFFERENT
ways of measuring geometric figures
The perimeter (notated “P”) of a
polygon is the sum of the lengths of its
sides
The area (notated “A”) of a polygon is
the number of square units it encloses
Many figures have formulas to calculate
their perimeter and area.
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Which do you need to know: area
or perimeter?
The amount of carpet for the basement floor
Area
The amount of fence for a dog run
Perimeter
The amount of paint for the bedroom
Area
The amount of Halloween lights to hang around the window
Perimeter
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General Formulas
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Problem 1
You want to frame a 5 in by 7 in picture with a 1-in-wide frame.
What is the perimeter of the picture?
What is the perimeter of the outside edge of the frame?
5 in
7 in
9 in
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Problem 1
Perimeter of a
rectangle has a formula: P=2l + 2w
P=2(5 in) + 2(7 in)
P=10 in + 14 in
Perimeter of the
picture is 24 inches
5 in
7 in
9 in
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Problem 1
Perimeter of a
rectangle has a formula: P=2l + 2w
P=2(7 in) + 2(9 in)
P=14 in + 18 in
Perimeter of the
picture is 32 inches
5 in
7 in
9 in
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Circles have special notation
and formulas
is the notation for circle. The
point that represents the center of
the circle is listed to the right of
the notation
How is W read?
Circle with center W
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Circles and Pi
The formulas for a circle involve the special number pi (). Pi is the ratio
of any circle’s circumference
(perimeter) to its diameter. Pi is an
irrational number.
= 3.1415926…
A close approximation is 22
7
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Problem 2 What is the
circumference and
area of the circle
at the right?
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Problem 2 15 inches is the
diameter, so we’ll need
to use the
circumference formula
with “d”
𝐶 = 𝜋(𝑑)
𝐶 = 𝜋 15 𝑖𝑛
𝐶 = 15𝜋 𝑖𝑛
This answer is exact
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Problem 2 15 inches is the
diameter, so we’ll need
to use the
circumference formula
with “d”
𝐶 = 𝜋(𝑑)
𝐶 = 𝜋 15 𝑖𝑛
𝐶 = 15𝜋 𝑖𝑛 ≈ 47.1 𝑖𝑛𝑐ℎ𝑒𝑠
This answer is
approximate
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Problem 2 What is the
circumference and
area of the circle
at the right?
The area formula
needs the radius,
which is one-half
the diameter
𝑟 = 7.5 𝑖𝑛
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Problem 2 What is the
circumference and area
of the circle at the right?
𝐴 = 𝜋𝑟2
𝐴 = 𝜋7.52
𝐴 ≈ 176.7 𝑖𝑛2
This is the approximate
answer
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Finding Area of a Rectangle
You are designing
a poster that will
be 3 yd wide and 8
ft high. How much
paper do you
need to make the
poster? Give your
answer to the
nearest square
foot.
Your units must be
the same.
1 𝑦𝑑 = 3 𝑓𝑡
3 𝑦𝑑 = 9 𝑓𝑡
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Finding Area of a Rectangle
Use the area for a
rectangle formula
𝐴 = 𝑙 𝑤
𝐴 = 9 𝑓𝑡 8 𝑓𝑡
𝐴 = 72 𝑓𝑡2
You need 72 𝑓𝑡2 of
paper to make the
poster
Your units must be
the same.
1 𝑦𝑑 = 3 𝑓𝑡
3 𝑦𝑑 = 9 𝑓𝑡
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The units of the
floor plan at the
right are in feet.
Find the perimeter
and area of each
room.
a. the kitchen
b. the bedroom
c. the bathroom
d. the closet