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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!

2
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Perimeter
•Any shape’s “perimeter” is the
outside of the shape…like a fence
around a yard.

3

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

4

Perimeter
•Triangles have 3 sides…add up each
sides length.

8
8

8+8+8=24
8 The Perimeter is 24
5

Perimeter
•A square has 4 sides of a fence
12

12 12

12+12+12+12=48
12
6

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

7

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

8

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

15
9

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

20
25
10

Other shapes
•Just add up EACH segment

10

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

11

Odd shapes
• Count ALL sides
• Remember if one side blank, it’s equal to its opposite
25+25=50 (for Length) 15+5+15+5=40 (for Width)

5

15

Perimeter=90
25
12

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

13

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)
14

Area of Squares/Rectangles
•Length x Width=Area

2

Length(2) xWidth(2) = 4 square units
15

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

16

Parallelogram Area
•Area=Base x Height
•(Area=length x width)
The diagonal line is NOT
5 the height!!!
Height (width)

8
BASE (length)
Base 8 x Height 5 = Area 40
17

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
18

Different Names/Same idea
•Length x Width = Area

•Side x Side = Area

•Base x Height = Area

19

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 5 = Area
4 x 5 = 20
Base
20

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

21

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

22

Area of a circle
•Area = piR^2
•Pi = 3.14 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

24


•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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