Formulas for
GeometryMr. Ryan
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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.
88
88+8+8=24The Perimeter is 24
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Perimeter
•A square has 4 sides of a fence
12 12
12
12
12+12+12+12=48
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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
2520
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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
25
15
5
25+25=50 (for Length) 15+5+15+5=40 (for Width)
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 units (ft, in, m)
2
3 4
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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)
BASE (length)
Height (width)
8
5
Base 8 x Height 5 = Area 40
The diagonal line is NOTthe height!!!
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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 missing)
Base
Height
Height
Base
8
5
½ Base x Height = Area½ (8) x 5 = Area 4 x 5 = 20
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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
Radius
5
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.