Transcript Perimeter, Area, and Circumference

Chapter 9
Geometry
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All rights reserved
Chapter 9: Geometry
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
Points, Lines, Planes, and Angles
Curves, Polygons, and Circles
Perimeter, Area, and Circumference
The Geometry of Triangles: Congruence,
Similarity, and the Pythagorean Theorem
Space Figures, Volume, and Surface Area
Transformational Geometry
Non-Euclidean Geometry, Topology, and Networks
Chaos and Fractal Geometry
9-3-2
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Chapter 1
Section 9-3
Perimeter, Area, and Circumference
9-3-3
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Perimeter, Area, and Circumference
•
•
•
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Perimeter of a Polygon
Area of a Polygon
Circumference of a Circle
Area of a Circle
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Perimeter of a Polygon
The perimeter of any polygon is the sum of
the measures of the line segments that form its
sides. Perimeter is measured in linear units.
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Perimeter of a Triangle
The perimeter P of a triangle with sides of
lengths a, b, and c is given by the formula
P = a + b + c.
b
a
c
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Perimeter of a Rectangle
The perimeter P of a rectangle with length l
and width w is given by the formula
l
P = 2l + 2w,
w
or equivalently
P = 2(l + w).
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Perimeter of a Square
The perimeter P of a square with all sides of
length s is given by the formula
s
P = 4s.
s
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Area of a Polygon
The amount of plane surface covered by a
polygon is called its area. Area is measured
in square units.
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Area of a Rectangle
The area A of a rectangle with length l and
width w is given by the formula
l
A = lw.
w
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Example: Rectangle
Find the perimeter and area of the rectangle
below.
15 ft.
7 ft.
Solution
Perimeter
P = 2l + 2w = 2(15) + 2(7) = 44 ft.
Area
A = lw = 15(7) = 105 ft.2
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Area of a Square
The area A of a square with all sides of
length s is given by the formula
s
P = s2.
s
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Area of a Parallelogram
The area A of a parallelogram with height h
and base b is given by the formula
A = bh.
h
b
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Area of a Trapezoid
The area A of a trapezoid with parallel bases
b and B and height h is given by the formula
b
1
A  h  B  b.
2
h
B
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Example: Area of a Parallelogram
Find the area of the trapezoid below.
7 cm.
5 cm.
Solution
13 cm.
1
1
A  h  B  b   (5)  7  13
2
2
1
2
 (5)  20   50 cm.
2
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9-3-15
Area of a Triangle
The area A of a triangle with base b and
height h is given by the formula
1
A  hb.
2
h
b
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Example: Area With Multiple Shapes
Find the area of the shaded region below.
4 in.
Solution
4 in.
Area of square – Area of triangle
1
s  bh
2
1
2
2
4  (4)(4)  16  8  8 in.
2
2
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9-3-17
Circumference of a Circle
The distance around a circle is called its
circumference.
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Circumference of a Circle
The circumference C of a circle of diameter d
is given by the formula.
C   d,
or equivalently
r
d
C  2 r ,
where r is a radius.
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Area of a Circle
The area A of a circle with radius r is given
by the formula.
A r .
2
r
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Example: Circle
Find the area and circumference of a circle
with a radius that is 6 inches long (use 3.14
as an approximation for pi).
Solution
Circumference
C  2 r  2 (6)  12  37.68 in.
Area
2
2
2
A   r   (6)  36  113.04 in.
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