Formulas for Geometry.ppt

Formulas for
Geometry
Mr. Ryan

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2
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!

3
Perimeter
• Any shape’s “perimeter” is
the outside of the
shape…like a fence around a
yard.

4
Perimeter
• To calculate the perimeter of
any shape, just add up
“each” line segment of the
“fence”.

5
Perimeter
• Triangles have 3 sides…add
up each sides length.
8
8
8
8+8+8=24
The Perimeter is 24

6
Perimeter
• A square has 4 sides of a
fence
12 12
12
12
12+12+12+12=48

7
Perimeter
• Sometimes, problems may
only give you two
measurements for a square
or rectangle.
• No problem…use the formula
for squares/rectangles (only!)

8
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

9
The Same!!
• If the bottom is 15…the top is…
15

10
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
25
20

11
Other shapes
• Just add up EACH segment
10
8 sides, each side 10 so 10+10+10+10+10+10+10+10=80

12
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

13
Area
• Area is the ENTIRE INSIDE
of a shape
• It is always measured in
“squares” (sq. inch, sq ft)

14
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

15
Area of Squares/Rectangles
• Length x Width=Area
2
Length(2) xWidth(2) = 4 square units

16
Parallelogram Area
• Same idea as squares &
rectangles, but they change
the words to Base
(length:bottom of shape) and
height (width)

17
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 NOT
the height!!!

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

19
Different Names/Same idea
• Length x Width = Area
• Side x Side = Area
• Base x Height = Area

20
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 = Area
½ (8) x 5 = Area
4 x 5 = 20

21
Area of a Circle
• Pi= 3.14
• Radius: from center (origin)
of circle to ANY side
• Area= pi x (Radius x Radius)

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

23
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

24
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

25

• 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.

26
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