Formulas for Geometry

Formulas for

GeometryMr. Ryan

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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!


Perimeter

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


Perimeter

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


Perimeter

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

88

88+8+8=24The Perimeter is 24


Perimeter

•A square has 4 sides of a fence

12 12

12

12

12+12+12+12=48


Perimeter

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

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


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


The Same!!

• If the bottom is 15…the top is…

15


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


Other shapes

•Just add up EACH segment

10

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


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


Area

•Area is the ENTIRE INSIDE of a shape

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


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


Area of Squares/Rectangles

•Length x Width=Area

2

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


Parallelogram Area

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


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!!!


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


Different Names/Same idea•Length x Width = Area

•Side x Side = Area

•Base x Height = Area


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


Area of a Circle

•Pi= 3.14•Radius: from center (origin) of circle to ANY side

•Area= pi x (Radius x Radius)


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


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


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


•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.

Formulas for Geometry

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