Area of Polygons and Circles

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Area of Polygonsand Circles
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Area (parallelogram) 
Area (rectangle)
 Area (triangle)
Area (square)
Area (trapezoid) 
Area (circle)
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When finding the area of any figure, the label of
the units is always "square" units.
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Be careful of problems that give "extra"
information.  In this problem, the 24 is NOT
needed to compute the area.
Area 280 units2 or 280 sq. units
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When working with parallelogram problems, be sure
that the height you are using is in fact
perpendicular (makes a right angle) to the base
(side) you are using.  In this problem, 8 is the
base and 9 is the height.  The side of 10 is not
used in this area.
Area 72 units2 or 72 sq. units
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It may be necessary, when working with an obtuse
triangle, to look outside the triangle to find
the height.  Notice how the height is drawn to an
extension of the base of the triangle.
Area 160 units2 or 160 sq. units
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When working with circles, be sure that you are
using the radius.  In this diagram, 10 is the
diameter.  The radius is half of the diameter.
3.14
Area 78.5 units2 or 78.5 sq. units
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When working with a trapezoid, the height may be
measured anywhere between the two bases.  Also,
beware of "extra" information.  The 35 and 28 are
not needed to compute this area.
Area 78.5 units2 or 78.5 sq. units
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Practice Problems
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5.
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6.
The area of a trapezoid is 28 sq. ft.  The bases
are 5 ft. and 9 ft.  What is the height of the
trapezoid in feet?
7.
The school band is selling pennants.  Each
pennant is cut in the shape of a triangle 4 feet
long and 1 foot high.  How many square feet of
fabric are needed to make 200 pennants? (Assuming
that there is no wasted fabric)
8.
Tom plans to make a strawberry shortcake to take
to a party.  The recipe calls for a 10 inch
diameter round pan.  Tom only has an 8 inch
square pan, a 9 inch square pan and a 10 inch
square pan.  Which pan comes closest in area to
the one that the recipe suggests?
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Perimeter and Circumference 
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Perimeter is the word used to describe the
distance around the outside of a figure.
To find the perimeter, add together the lengths
of all the sides of the figure.
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Example
For an art project at school, you need a piece of
string long enough to wrap around the outer edge
of this starfish.  What is the shortest possible
length of the string?
Perimeter 2 1.5 1 2 1.5 2 2 3
2.5 2  19.5 inches
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Circumference is the word used to describe the
distance around the outside of a circle.
3.14
Use when you know the radius.
Use when you know the diameter.
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Example
3.14
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C 3.14 12
C 37.68 units
Example
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C 2 3.14 5
C 31.4 units
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Practice Problems
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9.
Find the perimeter of this trapezoid.  
10.
A rectangular football field has side lines 120
yards long.  Each of the end lines is 160 feet
long.  What is the perimeter of the football
field?
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11.
The diameter of this circular placemat is 15
inches.  Find the circumference to the nearest
tenth of an inch?
12.
The pied piper and his friends are walking around
a track that is shaped like a regular pentagon.  
Each side measures 85 feet.  If they make 3
complete trips around the track, how far will
they have walked?