perimeterz

7/29/2019 Perimeterz

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Perimeter, perimeter formulas

Perimeter is of a figure is the length of all its sides. Not all figures have perimeter, for example globedoes not have perimeter. The standard notation for perimeter in math is the letter P

Perimeter of Square

Let's a square side is long a. Square have four equal sides so square perimeter is P = a + a + a+a or:

P = 4a

Perimeter of rectangle

Let's a rectangle sides are long a and b.The length of all its sides is P = a + b + a + b or:

P = 2a + 2b

Perimeter of parallelogram

Let's palallelogram sides are long a and bThe length of all its sides is P = a + b + a + b so parallelogram perimeter is:

P = 2a + 2b

As you can see the perimeter of the parallelogram is equal the perimeter of the rectangle.

Perimeter of isosceles trapezoid

Say the length of the parallel sides of a trapezoid are long a and b and the other two sides arelong c(As we know isosceles trapezoid has two equal sides).

P = a + b + c + c = a + b + 2c

Perimeter of equilateral triangle


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As we know equilateral triangles have 3 equal sides. So if the length of the side is a then theperimeter formula is P = a + a + a

P = 3a

Perimeter of parallelepiped

Parallelepiped is a figure that all sides are parallelogram.(Rectangular parallelepipeds is a figure thatsides are rectangles.)If bottom edges are long a and b then the perimeter of the bottom is P = 2a + 2b. Every

parallelepiped have two bottoms so the perimeter of the two bottoms is (2a + 2b).2 = 4a + 4b. Aswe know parameter is sum of all edges. So we have to add four times c

P = 4a + 4b + 4c

Perimeter of cube

Cube is a parallepiped that sides are squares(all edges are equal).So the perimeter of a cube is the number of edges * length.Every cube has 12 edges.So the perimeter formula of a cube is:

P = 12a

where a is the edge length.


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Area Formulas

(Math|Geometry| Area Formulas)

(pi= = 3.141592...)

Area Formulas

Note: "ab" means "a" multiplied by "b". "a2" means "a squared", which is the same as "a" times

"a".

Be careful!! Units count. Use the same units for all measurements.Examples

square = a2

rectangle = ab

parallelogram = bh

trapezoid = h/2 (b1 + b2)

circle = pir2

ellipse = pir1 r2

triangle=one half times the base length times the

height of the triangle
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equilateral triangle =

triangle given SAS (two sides and the opposite angle)= (1/2) a b sin C

triangle given a,b,c = [s(s-a)(s-b)(s-c)] when s = (a+b+c)/2 (Heron'sformula)

regular polygon = (1/2) n sin(360/n) S2

when n = # of sides and S = length from center to a corner

Units

Area is measured in "square" units. The area of a figure is the number ofsquares required to cover it completely, like tiles on a floor.

Area of a square = side times side. Since each side of a square is the same, itcan simply be the length of one side squared.

If a square has one side of 4 inches, the area would be 4 inches times 4inches, or 16 square inches. (Square inches can also be written in

2.)

Be sure to use the same units for all measurements. You cannot multiplyfeet times inches, it doesn't make a square measurement.

The area of a rectangle is the length on the side times the width. If the width is4 inches and the length is 6 feet, what is the area?

NOT CORRECT .... 4 times 6 = 24

CORRECT.... 4 inches is the same as 1/3 feet. Area is 1/3 feet times 6 feet =2 square feet. (or 2 sq. ft., or 2 ft

2).


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The formula for percentage is the following and it should be easy to use:

We will take examples to illustrate.Let us start with the formula on the left

An important thing to remember: Cross multiply

It means to multiply the numerator of one fraction by the denominator of the other fraction

Examples #1:

25 % of 200 is____

In this problem, of = 200, is = ?, and % = 25

We get:

is/200 = 25/100

Since is in an unknown, you can replace it by y to make the problem more familiar

y/200 = 25/100

Cross multiply to get y 100 = 200 25

y 100 = 5000

Divide 5000 by 100 to get y

Since 5000/100 = 50, y = 50

So, 25 % of 200 is 50

Examples #2:


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What number is 2% of 50 ?

This is just another way of saying 2% of 50 is___

So, set up the proportion as example #1:

is/50 = 2/100

Replace is by y and cross multiply to get:

y 100 = 50 2

y 100 = 100

Since 1 100 = 100, y = 1

Therefore, 1 is 2 % of 50

Examples #3:

24% of___ is 36

This time, notice that is = 36, but ofis missing

After you set up the formula, you get:

36/of = 24/100

Replace of by y and cross multiply to get:

36/y = 24/100

y 24 = 36 100

y 24 = 3600

Divide 3600 by 24 to get y

3600/24 = 150, y = 1500

Therefore, 24 % of 150 is 36

Now, we will take examples to illustrate how to use the formula for percentage on the right

Examples #4:


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To use the other formula that says part and whole, just remember the following:

The number afterofis always the whole

The number afteris is always the part

If I say 25 % of___ is 60, we know that the whole is missing and part = 60

Your proportion will will like this:

60/whole = 25/100

After cross multiplying, we get:

whole 25 = 60 100

whole 25 = 6000

Divide 6000 by 25 to get whole

6000/25 = 240, so whole = 240

Therefore, 25 % of 240 is 60

Examples #5:

___% of 45 is 9

Here whole = 45 and part = 9, but % is missing

We get:

9/45 = %/100

Replacing % by x and cross multiplying gives:

9 100 = 45 x

900 = 45 x

Divide 900 by 45 to get x

900/45 = 20, so x = 20

Here we go!. I hope these formula for percentage were helpful


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Decimals, Fractions and Percentages

Decimals, Fractions and Percentages are just different ways of showing the same

value:

A Halfcan be written...

As a fraction: 1/2

As a decimal: 0.5

As a percentage: 50%

A Quarter can be written...

As a fraction: 1/4

As a decimal: 0.25

As a percentage: 25%

Here, have a play with it yourself:


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View Larger

Example Values

Here is a table of commonly occuring values shown in Percent, Decimal and Fraction form:

Percent Decimal Fraction

1% 0.01 1/100

5% 0.05 1/20

10% 0.1 1/10

12% 0.125 1/8

20% 0.2 1/5

25% 0.25 1/4

331/3% 0.333...1/3

50% 0.5 1/2

75% 0.75 3/4

80% 0.8 4/5

90% 0.9 9/10

99% 0.99 99/100

100% 1

125% 1.255

/4

150% 1.5 3/2

200% 2
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Conversions

From Percent to Decimal

Toconvert from percent to decimal: divide by 100, and remove the "%" sign.

The easiest way to divide by 100 is to move the decimal point 2 places to the left. So:

From Percent To Decimal

move the decimal point 2 places to

the left, and remove the "%" sign.

From Decimal to Percent

Toconvert from decimal to percent: multiply by 100, and add a "%" sign.

The easiest way to multiply by 100 is to move the decimal point 2 places to the right.

So:

From Decimal To Percent

move the decimal point 2 places to

the right, and add the "%" sign.

From Fraction to Decimal

The easiest way toconvert a fraction to a decimalis to divide the top number by the bottomnumber (divide the numerator by the denominator in mathematical language)

Example: Convert 2/5 to a decimal

Divide 2 by 5: 2 5 = 0.4

Answer: 2/5 = 0.4
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From Decimal to Fraction

Toconvert a decimal to a fractionneeds a little more work.

Example: To convert 0.75 to a fraction

Steps Example

First, write down the decimal "over" the number 1 0.75 / 1

Then multiply top and bottom by 10 for every number after the decimal

point (10 for 1 number, 100 for 2 numbers, etc)0.75 100 / 1 100

(This makes it a correctly formed fraction) = 75 / 100

ThenSimplifythe fraction 3 / 4

From Fraction to Percentage

The easiest way toconvert a fraction to a percentageis to divide the top number by the

bottom number. then multiply the result by 100, and add the "%" sign.

Example: Convert 3/8 to a percentage

First divide 3 by 8: 3 8 = 0.375,

Then multiply by 100: 0.375 x 100 = 37.5

Add the "%" sign: 37.5%

Answer: 3/8 = 37.5%

From Percentage to Fraction

Toconvert a percentage to a fraction, first convert to a decimal (divide by 100), then use

the steps for converting decimal to fractions (like above).

Example: To convert 80% to a fraction

Steps Example
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Convert 80% to a decimal (=80/100): 0.8

Write down the decimal "over" the number 1 0.8 / 1

Then multiply top and bottom by 10 for every number after the decimal

point (10 for 1 number, 100 for 2 numbers, etc)0.8 10 / 1 10

(This makes it a correctly formed fraction) = 8 / 10

ThenSimplifythe fraction 4 / 5
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