1. Formulas for Geometry Mr. 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. 8 8
8+8+8=24
The Perimeter is 24 8
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Perimeter
A square has 4 sides of a fence 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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10. Square/Rectangle Formula
Perimeter=2(Length+Width)
P= 2(25+14) P=2(20+20)
P= P=40+40
P= P=80 14 20 25
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Other shapes
Just add up EACH segment 10
8 sides, each side 10 so =80
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Odd shapes
Count ALL sides
Remember if one side blank, it’s equal to its opposite
=40 (for Width)
25+25=50 (for Length) 5 15
Perimeter=90 25
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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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15. 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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18. 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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19. 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)
Height 5
Base 8
Height
½ Base x Height = Area
½ (8) x = Area
x = 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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22. 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 = 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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