DEV 108 Unit 4 Notes: Geometric Formulas

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DEV 108Unit 4 NotesGeometric Formulas
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Key Vocabulary Terms

• Area
• Circle
• Circumference
• Cube
• Cylinder
• Diagonal
• Diameter
• Hypotenuse
• Parallelogram
• Perimeter
• Pi

Polygon Pythagorean Theorem Quadrilaterals Radius
Rectangle Rectangular Prism Right
Angle Square Surface Area Triangle Volume
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Key Ideas with Measurement
Perimeter is the distance around the outside of
a figurethe black line of the picture
Perimeter is ALWAYS measured in plain units (ft,
yd, in, mi, cm, m, mm, etc)
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Key Ideas with Measurement
Area is the inside space of a two-dimensional
figurethe colored portion of the picture
Area is ALWAYS measured in square units (ft2,
yd2, in2, mi2, cm2, m2, mm2, etc)
There are two ways to write square unit Sq
units Units2
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Key Ideas with Measurement
Volume is the space inside a three-dimensional
figurethe stuff in the box
Volume is ALWAYS measured in cubic units (ft3,
yd3, in3, mi3, cm3, m3, mm3, etc)
There are two ways to write cubic units Cu
unit Units3
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Key Ideas with Measurement
Pythagorean measures are used to find the
missing side measurement of a right triangle.
Pythagorean measures are ALWAYS measured as
plain units (ft, yd, in, mi, cm, m, mm, etc)
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Two-Dimensional Figures
Diagonal
Circle
Triangle
radius
diameter
Hypotenuse
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Two-Dimensional Figure Formulas
Geometric Measures that you can find with 2-D
figures are
Perimeter the distance around the outside
Square P 4s Rectangle P 2L 2W Triangle
P a b c
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Two-Dimensional Figure Formulas
Geometric Measures that you can find with 2-D
figures are
Circumference the distance around the outside
of a circle
Circle C d ? or C 2 ? r
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Two-Dimensional Figure Formulas
Geometric Measures that you can find with 2-D
figures are
Area the space inside a figure
A bh A ½ bh
Squares and Rectangles A LW Triangles A ½
LW
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Two-Dimensional Figure Formulas
Geometric Measures that you can find with 2-D
figures are
Area the space inside a figure
Circles A ? r2
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Applying 2-D Formulas
28 in
Perimeter ___
49 in2
Area ___
A L W
P 4s
A 7 7 A 49 in2
P 4 7 P 28 in
HINT ALWAYS start with your formula
Dont forget to label your answers
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Applying 2-D Formulas
52 cm
Perimeter ___
133 cm2
Area ___
A L W
P 2L 2W
A 19 7 A 133 cm2
P 2(19) 2(7) P 38 14 P 52 cm
HINT ALWAYS start with your formula
Dont forget to label your answers
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Applying 2-D Formulas
18 m
Perimeter ___
5 m
5 m
3 m
12 m2
Area ___
4 m 4 m
A ½ L W
P a b c
A ( ½ )(3)(8) A 12 m2
P 5 5 8 P 18 m
HINT ALWAYS start with your formula
Dont forget to label your answers
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Applying 2-D Formulas
24 in
Perimeter ___
24 in2
Area ___
A ½ L W
P a b c
A ( ½ )(6)(8) A 24 in2
P 6 8 10 P 24 in
HINT ALWAYS start with your formula
Dont forget to label your answers
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Applying 2-D Formulas
62.8 m
Circumference ___
314 m2
Area ___
A ? r2
C d ?
A (3.14)(10)(10) A 314 m2
C (20)(3.14) C 62.8 m
HINT ALWAYS start with your formula
Dont forget to label your answers
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Applying 2-D Formulas
31.4 in
Circumference ___
78.5 in2
Area ___
A ? r2
C 2 ? r
A (3.14)(5)(5) A 78.5 in2
C (2)(3.14)(5) C 31.4 in
HINT ALWAYS start with your formula
Dont forget to label your answers
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Three-Dimensional Figures
The only geometric measure that we will be
finding with 3-D figures is Volume.
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Three-Dimensional Figure Formulas
The geometric measure that you will be finding
with 3-D figures is
Volume the space occupied on the inside of a
3-D figurethe stuff in the box or can
V L W H
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Three-Dimensional Figure Formulas
The geometric measure that you will be finding
with 3-D figures is
Volume the space occupied on the inside of a
3-D figurethe stuff in the box or can
r
V ? r2h
h
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Applying 3-D Formulas
V L W H
V 3 14 11 V 462 in3
HINT ALWAYS start with your formula
Dont forget to label your answers
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Applying 3-D Formulas
V L W H
V 20 ? 20 ? 20 V 8,000 mm3
HINT ALWAYS start with your formula
Dont forget to label your answers
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Applying 3-D Formulas
6 mm
V ? r2h
V (3.14)(6)(6)(11) V 1,243.44 mm3
11 mm
HINT ALWAYS start with your formula
Dont forget to label your answers
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Pythagorean Theorem
The Pythagorean Theorem is used to find the
missing measure of a side of a right triangle.
The two legs of the triangle are always a
and b
The hypotenuse of the triangle is always c
Pythagorean Formula
a2 b2 c2
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Applying the Pythagorean Theorem
Start with your formula
a2 b2 c2
32 42 c2 9 16 c2 25 c2 25 c
To get from c2 to ctake the square root of the
number
5 in c
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Applying the Pythagorean Theorem
Start with your formula
15 cm
12 cm
a2 b2 c2
122 b2 152 144 b2 225 b2 81 b 81
b
To get from b2 to btake the square root of the
number
b 9 cm
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Using Geometric Formulas Successfully
Step 1 Draw and label a picture or diagram
for your problem
Step 2 Write down the appropriate formula
Step 3 Plug in your numbers and chug through
the arithmetic
Step 4 Check to see that your answer makes
sense
Step 5 Label your final answer
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Application Problems using Geometric Formulas
Bud wants to fence in a dog run. If the dog run
is 15 ft by 10 ft, how much fencing will Bud need?
P 2L 2W
P 2(15) 2(10) P 30 20 P 50 ft
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Application Problems using Geometric Formulas
How much rice can fit in a container that has a
diameter of 4 inches and a height of 7 inches?
V ? r2 h
V (3.14)(4)(4)(7) V 351.68in3
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Application Problems using Geometric Formulas
How much felt will be needed to cover the top of
a board that is 11 inches by 8 inches?
A L ? W
A (11)(8) P 88 in2
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Application Problems using Geometric Formulas
What is the diameter of a circle that has an area
of 153.86 cm2?
A ? r2
153.86 cm2 (3.14)(r2) 153.86 3.14r2
3.14 3.14 49 r2 7 r
Remember that d 2r therefore d 14 cm
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Review the things that you need to review.
Study the things that you need to spend more time
on.
Ask questions about things you dont understand.
PRACTICEPRACTICEPRACTICE