Formulas for
Geometry
Mr. Ryan
Don’t Get Scared!!!
•Evil mathematicians have created
formulas to save you time. But, they
always change the letters of the
formulas to scare you!
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Perimeter
•Any shape’s “perimeter” is the
outside of the shape…like a fence
around a yard.
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Perimeter
•To calculate the perimeter of any
shape, just add up “each” line
segment of the “fence”.
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Perimeter
•Triangles have 3 sides…add up each
sides length.
8
8
8
8+8+8=24
The Perimeter is 24
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Perimeter
•A square has 4 sides of a fence
12
12
12
12+12+12+12=48
12
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Perimeter
•Sometimes, problems may only give
you two measurements for a square
or rectangle.
•No problem…use the formula for
squares/rectangles (only!)
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Remember
• Squares ALL sides are equal…so if they give you
one side, you know ALL the sides
• Length=the Largest side
• If they “leave” numbers out, they are equal to
their opposite side. If they give you the bottom of a
square/rectangle type shape then the top is the
same
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The Same!!
•If the bottom is 15…the top is…
15
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Square/Rectangle Formula
• Perimeter=2(Length+Width)
• P= 2(25+14)
P=2(20+20)
• P= 50+28
P=40+40
• P= 78
P=80
14
20
25
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Other shapes
•Just add up EACH segment
10
8 sides, each side 10 so 10+10+10+10+10+10+10+10=80
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Odd shapes
• Count ALL sides
• Remember if one side blank, it’s equal to its opposite
15+5+15+5=40 (for Width)
25+25=50 (for Length)
5
15
25
Perimeter=90
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Area
•Area is the ENTIRE INSIDE of a
shape
•It is always measured in “squares”
(sq. inch, sq ft)
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AREA
• Square units means that “that” many squares fit inside that shape (if measured
in feet…it’s feet…if meters…it’s meters. In this example the area is 4 square
units…note 4 squares fit)
1
2
3
4
2 units (ft, in, m)
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Area of Squares/Rectangles
•Length x Width=Area
2
Length(2) xWidth(2) = 4 square units
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Parallelogram Area
•Same idea as squares & rectangles,
but they change the words to Base
(length:bottom of shape) and height
(width)
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Parallelogram Area
•Area=Base x Height
•(Area=length x width)
The diagonal line is NOT
the height!!!
5
Height (width)
8
BASE (length)
Base 8 x Height 5 = Area 40
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REAL formula for area of squares
•Area= S^2
•Area= Side x Side (side squared)
(just a different way of saying
length x width)
Side one
Side two
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Different Names/Same idea
•Length x Width = Area
•Side x Side = Area
•Base x Height = Area
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Area of a Triangle
•½ Base x Height = Area
•(It’s ½ because ½ of the “square” is
Height
missing)
5
Base
8
Height
½ Base x Height = Area
½ (8) x 5 = Area
4
x
5 = 20
Base
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Area of a Circle
•Pi= 3.14
•Radius: from center (origin) of
circle to ANY side
•Area= pi x (Radius x Radius)
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Circumference of a Circle
• Perimeter/Circumference = pi x diameter
• Pi is always 3.14
• Circumference is a fancy name for perimeter
• The diameter is a line from one side to the other
side of a circle through its origin (It’s twice the
radius)
If the radius is 5, then the diameter is 10
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Area of a circle
•Area = piR^2
•Pi = 3.14 and R=Radius
5
Radius
Area=3.14 x (5 x 5)
Perimeter = 3.14 x 10
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You’re Done
•Squares, rectangles and parallelograms
area are almost the same (LxW)
•Triangles are ½ cause your missing ½
•Circles have fancy names, but just follow
the formula
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
•For most tests you will have the
formulas given to you. Just
remember which one to use for which
shape and you’ll do fine.
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