Area, Volume, and Surface Area

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Area, Volume, and Surface Area
Section 9.3
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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 A 3 2 units2 A 6 units2
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3
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Area Formulas
Triangle
Parallelogram
The diagonal of a parallelogram forms 2
congruent triangles.
3 2 6
A bh
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More Area Formulas
Trapezoid

area side side
A s s s 2
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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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Area of a Circle
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Area of a Circle
Notice the rectangular shape.
A lw
A (?r)r
A ?r 2
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Perimeter/ Circumference
Plane Figure
Drawing
Area
P a b c
Triangle
P a b c d
Parallelogram
A bh
P 2l 2w
Rectangle
A lw
P 4s
Square
A s2
P a b c d
Trapezoid
C ? d or 2? r
A ?r 2
Circle
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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
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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A polyhedron is a solid formed by the
intersection of a finite number of planes.
Surface Area
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 inch
1 centimeter
1 centimeter
1 inch
1 centimeter
1 inch
1 cubic centimeter
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
Volume
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Circular Cylinder
height
radius
Volume

V ?r2h
SA 2? r h 2?r2
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Cone
height
radius
Volume

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Square-Based Pyramid
height
side
Volume

B area of base, p perimeter, l slant
height
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Volume is always measured in cubic units.
Surface area is always measured in square units.
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