formulas for geometry
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Formulas for Geometry. Mr. Ryan. Visit www.worldofteaching.com for more free powerpoints. Student Expectations. 6 th Grade 6.4.8A Estimate measurements (including circumference) and evaluate reasonableness of results. 7 th Grade - PowerPoint PPT PresentationTRANSCRIPT
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Formulas for
GeometryMr. Ryan
Visit www.worldofteaching.com for more free powerpoints
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Student Expectations
6th Grade• 6.4.8A Estimate measurements (including
circumference) and evaluate reasonableness of results.
7th Grade• 7.4.9A Estimate measurements and solve
application problems involving length (including perimeter and circumference) and area of polygons and other shapes.
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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.