Winpossible New York, New York, US,

November 9, 2008

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This is a part of the interactive online tutorial for Geometry learning with the help of audio visual lessons. It has been created to help you learn the concept, perception with explanations and includes solution to practice questions from the topic of ‘Perimeter and Circumference’. The mini-lessons here include: Getting started, Perimeter of a Polygon, Circumference of a Circle, Effect of dimension changes on perimeter, Real World Applications.

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- Mathematics > Geometry

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This is a part of the interactive online tutorial for Geometry learning with the help of audio visual lessons. It has been created to help you learn the concept, perception with explanations and includes solution to practice questions from the topic of ‘Perimeter and Circumference’. The mini-lessons here include: Getting started, Perimeter of a Polygon, Circumference of a Circle, Effect of dimension changes on perimeter, Real World Applications.

This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Getting started.

In this mini-lesson we cover the basics of a monomial, polynomial and the degree of a polynomial, as simply as possible and with the help of a number of examples. Some of the basic points in this lesson are mentioned below. Not that this might seem complicated here in text, but once you have instructor explain it to you in their voice and handwriting in the video, it will be easy to follow. Here are some of the basics for you to keep in mind:

In this mini-lesson we cover the basics of a monomial, polynomial and the degree of a polynomial, as simply as possible and with the help of a number of examples. Some of the basic points in this lesson are mentioned below. Not that this might seem complicated here in text, but once you have instructor explain it to you in their voice and handwriting in the video, it will be easy to follow. Here are some of the basics for you to keep in mind:

- ‘Monomial’ refers to a polynomial that has only a single (mono) term and the product of multiplying monomials together also results in a monomial e.g. x, 2x, xy, (10xy
^{4})/3. - ‘Polynomials’ refer to mathematical expressions that contain multiple terms x + 5, 2x – 5, (5xyz
^{3})/4 + 7x etc. - The degree of a term is the sum of the powers of each variable in the term. For example, the polynomial 5x
^{4}+ 2x^{3}– x + 7 has four terms. The first term has a degree of 4, the second term has a degree of 3, the third term has a degree of 1, and a last term has a degree of 0. - When a polynomial is expressed as a sum or difference of terms, the term with the highest degree, is the degree of the polynomial. Therefore, the polynomial has a degree of 4 which is the highest degree of any term.
- While adding or subtracting polynomials, remember that you can only combine 'like terms.' 'Like terms' contain the same variables and differ by the numeric coefficient in the left, e.g. 4x and 6x are like terms, and can be added to get 10x.
- Multiplying polynomials is a little more complicated, and involves adding up the products of multiplying each term in the first polynomial by each term in the second polynomial. The mini-lesson also explains the concept of ‘FOIL’, which is short form of "First, Outside, Inside, Last" and refers to which terms you multiply together and add up when multiplying two polynomials, each composed of two monomials. Again, this may appear little complicated here in text, but it will be easy to follow once you hear the instructor explain it in the video below.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Algebra I. Click on the video below to go through it. If you like it, you can buy our online course in Algebra I by clicking here.

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Getting Started - Perimeter and Circumference.

This mini-lesson content introduces and walks you through the basic concepts about the perimeter and circumference. You'll learn to practice with perimeter and circumference using some examples, practice questions with solution, helped by instructor using audio video method and his own handwriting that brings in an element of real-class room experience.

Perimeter and circumference are the measure of any two dimensional object or closed shape. E.g. To find the perimeter of any polygon, find the sum of the lengths of the sides. Let us look at the case of a quadrilateral, with*a*, *b*, *c*, and *d* as the lengths of its sides. The perimeter for this is the sum of all the sides i.e.

*P* = *a* + *b* + *c* + *d*

In case of a circle, the perimeter is called circumference. The perimeter of circle is

*C* = ?*d* or 2?*r*

where*d* is the diameter or *r* is the radius of the circle.

This mini-lesson content introduces and walks you through the basic concepts about the perimeter and circumference. You'll learn to practice with perimeter and circumference using some examples, practice questions with solution, helped by instructor using audio video method and his own handwriting that brings in an element of real-class room experience.

Perimeter and circumference are the measure of any two dimensional object or closed shape. E.g. To find the perimeter of any polygon, find the sum of the lengths of the sides. Let us look at the case of a quadrilateral, with

In case of a circle, the perimeter is called circumference. The perimeter of circle is

where

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Perimeter of a Polygon.

In this section; with the help of some examples and solution, we'll explore how to calculate the perimeter of the polygons. The perimeter is one dimensional and measured in linear units such as feet, meters or similar units. To find the perimeter of a polygon, follow these simple steps:*P*' is the perimeter, '*S*' is the length of each side and '*n*' stands for the number of sides of the polygon:

*P* = *S*_{1}+*S*_{2}+*S*_{3}+....+*S*_{n}

The perimeter of a pentagon*ABCDE* with each side measuring 3cm, is 15cm. The perimeter of a rectangle is the distance around the outside of the rectangle. It has four sides and opposite sides are congruent. If the length of a rectangle is *l* and the width is *w*, then the perimeter can be calculated by

*P* = *l* + *w* + *l* + *w*

or

*P* = 2(*l* + *w*)

E.g., to calculate the perimeter of the rectangle*ABCD*, having length *CD* = 9 cm and width *BC* = 4 cm, substitute 9 for *l* and 4 for *w* in above expression. It comes to *P* = 2(9 + 4), and that gives 26cm.
similarly, if a is the measure of the side of a square, then perimeter is given by

*P* = *a* + *a* + *a* + *a* = 4*a*

for example, if each side of a square is 10 cm, then the perimeter is*P* = 4 × 10, which works out to 40cm.

In this section; with the help of some examples and solution, we'll explore how to calculate the perimeter of the polygons. The perimeter is one dimensional and measured in linear units such as feet, meters or similar units. To find the perimeter of a polygon, follow these simple steps:

- Measure the length of each side of the shape using the same unit of measurement.
- Add all the lengths of each side together.
- Write the answer using the same unit of measurement or an equivalent unit of measurement.

The perimeter of a pentagon

or

E.g., to calculate the perimeter of the rectangle

for example, if each side of a square is 10 cm, then the perimeter is

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Circumference of a Circle.

In this section, we will focus on the basics about a circle, radius, and circumference. You'll also learn the mathematical term pi and formula for the circumference of circles. A circle is a shape with all the points at same distance from the center and the distance around a circle is called the circumference. The distance across a circle through the center is called the diameter. The radius of a circle is the distance from the center of a circle to any point on the circle. The diameter of a circle is twice as long as the radius and this relationship is expressed in the formula:

*d* = 2*r*

where*d* is the diameter and *r* is the radius.

If points*A*, *B*, and *C* are on the circle with center *O*, then

*OA* = *OB* = *OC* = *r*

to find circumference, we multiply pi (?) and the diameter of the circle i.e.

* C* = ?*d*

Given the circumference of a circle 220 cm, you can work out the diameter, which comes to 70 cm. You can also find the circumference of a circle, when the radius is given by*r*. The formula for finding circumference is:

*C* = 2?*r*

For example, if the radius of a circle is 3.5 units, then circumference of a circle is 7? units.

In this section, we will focus on the basics about a circle, radius, and circumference. You'll also learn the mathematical term pi and formula for the circumference of circles. A circle is a shape with all the points at same distance from the center and the distance around a circle is called the circumference. The distance across a circle through the center is called the diameter. The radius of a circle is the distance from the center of a circle to any point on the circle. The diameter of a circle is twice as long as the radius and this relationship is expressed in the formula:

where

If points

to find circumference, we multiply pi (?) and the diameter of the circle i.e.

Given the circumference of a circle 220 cm, you can work out the diameter, which comes to 70 cm. You can also find the circumference of a circle, when the radius is given by

For example, if the radius of a circle is 3.5 units, then circumference of a circle is 7? units.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Effect of dimension changes on perimeter.

In this mini-lesson; you'll have the instructor explain in their voice and handwriting in the video, how change in dimension in a figure affects the perimeter, E.g., the perimeter of a square will be doubled, if its side is doubled. It includes examples with solution for in-depth understanding. Let us look at example of a rectangle whose length is 5 times of its width. If the length is increased by 2 inches and width is decreased by 1 inch, the perimeter is 38 inches, What are the dimensions of original rectangle.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

In this mini-lesson; you'll have the instructor explain in their voice and handwriting in the video, how change in dimension in a figure affects the perimeter, E.g., the perimeter of a square will be doubled, if its side is doubled. It includes examples with solution for in-depth understanding. Let us look at example of a rectangle whose length is 5 times of its width. If the length is increased by 2 inches and width is decreased by 1 inch, the perimeter is 38 inches, What are the dimensions of original rectangle.

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Real World Applications.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

In this section, you'll be explained how real world problem can be solved by making use of the learning earlier about the perimeter, properties and relationships among figures in this mini-lesson. Note that this might seem complicated here in text, but once you have instructor explain it to you in their voice and handwriting in the video, you will find it much simpler. Explanations of the example exercises followed by practice problems with solution provide you additional help to enhance the skill and to become confident at solving problems and quizzes.

More commonly the perimeter and circumference formulas may be used. Look at an example, how you can compare the distance covered by two persons who run around any given figure when the measures of the sides of the figure are known. For example, if Tom runs around a square of side 60 m and John runs around a rectangle having length 75 m and width 45 m., both of them cover the same distance 240 m.

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