Transcript Chapter 9: Geometry and Measurement

Section 9.3
Area, Volume, and Surface
Area
Area of a Rectangle
Area is measured in square units. A
square unit is a square one unit on each
side.
For example, start with a rectangle with
length (l) 3 units and width (w) 2 units.
A = l •w
2
3
A = 3 • 2 units2
A = 6 units2
2
Area
Formulas
Rectangle
Parallelogram
2
Triangle
2
3
2
3
The diagonal of
a parallelogram
3
3•2 = 6
A = lw
forms 2
2
congruent triangles.
3
3•2 = 6
A = bh
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(3 • 2) = 3
2
1
A = 2 bh
3
More Area
Formulas
Trapezoid
B
Square
h
side
B
b
+ b
side
area = side • side
A = s • s = s2
1
(B  b )
2
1
A = (B  b )h
2
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Helpful Hint
Area is always measured in square units.
When finding the area of figures, check to
make sure that all measurements are the
same units before calculations are made.
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r
Given a circle of radius, r, the
circumference is C = 2 r.
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Dividing the circle into 4 equal
sectors, half the circumference, r,
is blue and the other half is red.
8 equal sectors
r
r
r
r
r
r
Area of a Circle
32 equal sectors
16 equal sectors
r
r
r
r
r
r
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64 equal sectors
128 equal sectors
r
r
r
r
r
r
Area of a Circle
n
2 equal sectors
Notice the rectangular shape.
r
A = lw
A = (r)r
r
r
A = r 2
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Plane Figure
Triangle
Parallelogram
Rectangle
Square
Trapezoid
Circle
Drawing
Perimeter/
Circumference
P=abc
Area
A=
1
bh
2
P=abcd
A = bh
P = 2l  2w
A = lw
P = 4s
P=abcd
C =  d or 2 r
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A = s2
A=
1
(B  b )h
2
A = r 2
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Volume
Volume measures the number of cubic
units that fill the space of a solid. The
volume of a box or can is the amount of
space inside.
Volume can be used to describe the
amount of juice in a pitcher or the amount
of concrete needed to pour a foundation for
a house.
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Surface Area
A polyhedron is a solid formed by the
intersection of a finite number of planes.
The surface area of a polyhedron is the
sum of the areas of the faces of the
polyhedron.
Surface area is measured in square units.
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The volume of a solid is the number of
cubic units in the solid.
1 centimeter
1 centimeter
1 centimeter
1 cubic centimeter
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1 inch
1 inch
1 inch
1 cubic inch
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Rectangular Solid
height
width
length
Volume = length  width  height
V = lwh
SA = 2lh + 2wh + 2lw
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Cube
side
side
side
Volume = side  side  side
V = s3
SA = 6s3
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Sphere
radius
4
Volume =    (radius)3
3
4 3
V = r
3
SA = 4 r 2
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Circular Cylinder
height
radius
Volume =   (radius)2  (height)
V = r2h
SA = 2 r h + 2r2
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Cone
height
radius
1
Volume =    (radius)2  (height)
3
1 2
V = r h
3
SA =  r r  h   r
2
2
2
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Square-Based Pyramid
height
side
1
Volume =  (side )2  height
3
1
V = s 2h
3
B = area of base,
1
SA = B  pl p = perimeter,
l = slant height
2
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Helpful Hint
Volume is always measured in cubic units.
Surface area is always measured in square
units.
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