Formulas geometry

Formulas for Formulas for GeometryGeometry

DonDon’’t Get t Get Scared!!!Scared!!!

Evil mathematicians have created Evil mathematicians have created formulas to save you time. But, they formulas to save you time. But, they always change the letters of the always change the letters of the formulas to scare you!formulas to scare you!

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PerimeterPerimeterAny shapeAny shape’’s s ““perimeterperimeter”” is the outside is the outside of the shape…like a fence around a of the shape…like a fence around a yard.yard.


PerimeterPerimeterTo calculate the perimeter of any To calculate the perimeter of any shape, just add up shape, just add up ““eacheach”” line segment line segment of the of the ““fencefence””..


PerimeterPerimeterTriangles have 3 sides…add up each Triangles have 3 sides…add up each sides length.sides length.


88

88+8+8=24The Perimeter is 24

PerimeterPerimeterA square has 4 sides of a fenceA square has 4 sides of a fence


12 12

12

12

12+12+12+12=48

PerimeterPerimeterSometimes, problems may only give you Sometimes, problems may only give you two measurements for a square or two measurements for a square or rectangle.rectangle.

No problem…use the formula for No problem…use the formula for squares/rectangles (only!)squares/rectangles (only!)


RememberRemember

Squares ALL sides are equal…so Squares ALL sides are equal…so if they give you one side, you if they give you one side, you know ALL the sidesknow ALL the sides

Length=the Largest sideLength=the Largest side

If they If they ““leaveleave”” numbers out, they numbers out, they are equal to their opposite side. are equal to their opposite side. If they give you the bottom of a If they give you the bottom of a square/rectangle type shape square/rectangle type shape then the top is the samethen the top is the same


The Same!!The Same!!

If the bottom is 15…the top If the bottom is 15…the top is…is…


15

Square/Rectangle Square/Rectangle FormulaFormula

Perimeter=2(Length+Width)Perimeter=2(Length+Width)P= 2(25+14) P= 2(25+14) P=2(20+20)P=2(20+20)P= 50+28P= 50+28 P=40+40 P=40+40P= 78P= 78 P=80 P=80


14

2520

Other shapesOther shapes

Just add up EACH segmentJust add up EACH segment


10

8 sides, each side 10 so 10+10+10+10+10+10+10+10=80

Odd shapesOdd shapes

Count ALL sidesCount ALL sides

Remember if one side blank, itRemember if one side blank, it’’s equal to its s equal to its oppositeopposite


25

15

5

25+25=50 (for Length) 15+5+15+5=40 (for Width)

Perimeter=90

AreaAreaArea is the ENTIRE INSIDE of a shapeArea is the ENTIRE INSIDE of a shape

It is always measured in It is always measured in ““squaressquares”” (sq. (sq. inch, sq ft)inch, sq ft)


AREAAREA

Square units means that Square units means that ““thatthat”” many squares fit inside that many squares fit inside that shape (if measured in feet…itshape (if measured in feet…it’’s feet…if meters…its feet…if meters…it’’s meters. s meters. In this example the area is 4 square units…note 4 squares fit)In this example the area is 4 square units…note 4 squares fit)


1

2 units (ft, in, m)

2

3 4

Area of Area of Squares/RectanglesSquares/Rectangles

Length x Width=AreaLength x Width=Area


2

Length(2) xWidth(2) = 4 square units

Parallelogram Parallelogram AreaArea

Same idea as squares & rectangles, but Same idea as squares & rectangles, but they change the words to Base they change the words to Base (length:bottom of shape) and height (length:bottom of shape) and height (width)(width)


Parallelogram Parallelogram AreaArea

Area=Base x HeightArea=Base x Height

(Area=length x width)(Area=length x width)


BASE (length)

Height (width)

8

5

Base 8 x Height 5 = Area 40

The diagonal line is NOTthe height!!!

REAL formula for area REAL formula for area of squaresof squares

Area= S^2Area= S^2

Area= Side x Side (side squared) (just a Area= Side x Side (side squared) (just a different way of saying length x width)different way of saying length x width)


Side one

Side two

Different Names/Same Different Names/Same ideaidea

Length x Width = AreaLength x Width = Area

Side x Side = AreaSide x Side = Area

Base x Height = AreaBase x Height = Area


Area of a TriangleArea of a Triangle

½ Base x Height = Area½ Base x Height = Area

(It(It’’s ½ because ½ of the s ½ because ½ of the ““squaresquare”” is is missing)missing)


Base

Height

Height

Base

8

5

½ Base x Height = Area½ (8) x 5 = Area 4 x 5 = 20

Area of a CircleArea of a CirclePi= 3.14Pi= 3.14

Radius: from center (origin) of circle to Radius: from center (origin) of circle to ANY sideANY side

Area= pi x (Radius x Radius)Area= pi x (Radius x Radius)


Circumference of Circumference of a Circlea Circle

Perimeter/Circumference = pi x Perimeter/Circumference = pi x diameterdiameter

Pi is always 3.14Pi is always 3.14

Circumference is a fancy name for Circumference is a fancy name for perimeterperimeter

The diameter is a line from one side The diameter is a line from one side to the other side of a circle through to the other side of a circle through its origin (Itits origin (It’’s twice the radius)s twice the radius)


If the radius is 5, then the diameter is 10

Area of a circleArea of a circle

Area = piR^2Area = piR^2

Pi = 3.14 and R=RadiusPi = 3.14 and R=Radius


Radius

5

Area=3.14 x (5 x 5) Perimeter = 3.14 x 10

YouYou’’re Donere Done

Squares, rectangles and Squares, rectangles and parallelograms area are parallelograms area are almost the same (LxW)almost the same (LxW)Triangles are ½ cause Triangles are ½ cause your missing ½your missing ½Circles have fancy Circles have fancy names, but just follow names, but just follow the formulathe formula


For most tests you will have the For most tests you will have the formulas given to you. Just remember formulas given to you. Just remember which one to use for which shape and which one to use for which shape and youyou’’ll do fine.ll do fine.


Formulas geometry

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