Stephanie Wight

First Edition

Math & MeasurementsCalculating the Perimeter and Areaof a Rectangle

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About the Author

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! My name is Stephanie Wight, and I am a fourth grade teacher at Washington Elementary School in Warsaw, Indiana. I graduated in 2017 from Indiana University with my Bachelors Degree in Elementary Education with a Math Concentration. My favorite things to do are spending time with friends and family, being at school and teaching, and being outside in the sun. I love teaching math, and I love using technology in my classroom. Technology helps enhance learning and makes it fun for students. I hope you have as much fun reading and learning from this eBook as I did writing it!

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Measurement

Measurement is the action of measuring the size, length, or amount of something. The standards of fourth grade math states that students should understand perimeter and area, as well as measuring volume, capacity, time and money. Throughout this book, we will focus on learning how to find the area and perimeter of a rectangle. The study of measurement is important because of its uses in many aspects of everyday life. Students develop and use the formulas for calculating perimeters and areas of rectangles.

1 In chapter 1 of Math and Measurements, we will be discussing how to find the perimeter of a rectangle. Pay close attention, and read carefully. Try your best to work with your own piece of paper and to go through the problems and write them out on your own as well. If you become confused, please read it over again, and if confusion continues, bring your questions to your teacher for further help! Perimeter is so fun to learn, enjoy!

Perimeter

What We Will Do In This Section

1. Learn the definition of perimeter

2. Learn the equation of perimeter

3. Practice using the equation by doing examples on how to find the perimeter of a rectangle

4. Learn about how perimeter can be used in real life situations

5. Summarize what we learned

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What Is Perimeter?

The perimeter is the distance around a two dimensional shape. It is the continuous line forming the boundary of a shape.

Example:

The perimeter of this rectangle is represented by the black lines.

What is the equation to finding the perimeter of a rec-tangle? Flip to the next page to find out!

Section 1

Perimeter

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How to find the Perimeter of a Rectangle

The perimeter of a rectangle can be found by adding together all four of the edges. The sides can be broken up into length and width. Each rectangle contains two lengths and two widths, therefore the equation to find the perimeter of a rectan-gle is:

Perimeter = length + length + width + width

or it can be abbreviated into

P = l + l + w + w

If we put this equation into practice using the previous rectan-gle, it will look like this

Perimeter = length + length + width + width

Let’s substitute some numbers in!!!

For this rectangle, the equation will be

P= 8 + 8 + 4 + 4

P=24 cm

The sum of all of the sides together, or the perimeter, is 24!

Another way to write the equation for perimeter is:

P= 2(l + w)

Therefore, this square would be

P= 2(8 + 4)

P= 2(12)

P=24 cm

length

length

widthwidth

8 cm

8 cm

4 cm 4 cm

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Here is another example

Here is how to solve the perimeter for this rectangle:

P= l + l + w + w

P= 10 + 10 + 3 + 3

P= 26

OR

P= 2(l + w)

P= 2(10+3)

P= 2(13)

P= 26

If you are confused or want to see a visual example, please watch this widget on how to find perimeter. He goes over it with a square, but it is the same concept.

Enjoy!

3 cm

3 cm

10 cm10 cm

INTERACTIVE 1.1 Perimeter You-tube Video

This math teacher goes over the concept of finding the perimeter of a one dimensional shape.

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Perimeter can differ in lengths, meaning it can be a measurement of centimeters, inches, feet, miles, and many more forms of measurement. In some instances, you may have to use a ruler to find the measurements of the length and width. Always make sure to label your an-swers according to its measurement.

Many students question the purpose in learning how to find the perimeter of shapes. First of all, learning how to find perimeter will make other math equations that you will learn in the future much easier. Also, there will be times in your life when the perimeter will be necessary to understand!

In the Widget on the next page, make sure to look through the pictures at the different forms that perimeter can be used.

How can Perimeter be used in real life situations?

In order to know how much fence is needed to surround the pool, one must measure the perimeter of the border of the pool area. Once they know the measurements, they will be ready to order the amount of feet necessary.

GALLERY 1.1 Perimeter in the Real World

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What did you learn?

You should have learned that perimeter is a term to describe the distance all the way around the shape. It expresses the measurement of each side of the shape.

You should have also learned that the equation to find the perimeter of a rectangle is:

Perimeter = length + length + width + width

Remember that perimeter is a useful tool that will be needed to know throughout your life. Whether you are installing carpet, or trying to build a around your house, or you are simply trying to buy a rug for your living room, knowing about the perimeter of a rectan-gle will help you in many ways.

What We Will Do In This Section

1. Learn the definition of area

2. Learn the equation used to find area of a rectangle

3. Go over examples using the equation and solve to find the area

4. Discover ways area is used in everyday life

5. Review what was taught in this section

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What is Area?

The area of a shape is the number of square units needed to cover the surface of a two dimensional shape.

Example:

What is highlighted in blue is known as the area of the rectangle.

Flip to the next page to learn about the equation of how to learn the area of a rectangle!

Section 2

Area

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How to find the Area of a Rectangle

The sides of a rectangle can be broken up into length and width. Make the length the longer edges, and make the width the shorter edges. Each rectangle contains two lengths and two widths, however, instead of adding up all of the numbers, we will multiply. To find the area of a rectangle, multiply the length times the width.

Area = length x width

If we put this equation into practice using the previous rectan-gle, it will look like this

Area = l x w

Let’s substitute some numbers in!!!

The equation to find the area of this rectangle will be:

A = l x w

A = 2 ft x 2 ft

A= 4 ft

This means that it would take 4 square inch units to cover the entire rectangle, which would look like this.

Because it is covered in surface area, you would write the final answer as 4 square ft.

l

w

2 ft

2 ft

2 ft

2 ft

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Let’s try another practice one, and make it a little bit harder!

For this rectangle, the equation will be

A = 5 cm x 3 cm

A = 15 square cm

When you multiply the length times the width, you get the area, which is 15. This means that it would take 15 square cm units to cover the entire rectangle, which would look like this:

If you take the time to count out all of the squares within the rec-tangle, it would equal 15 squares.

Once again, just like finding the perimeter, you have to be care-ful and make sure that you label the measurements, whether it is in cm, in, ft, or any others.

Also, in area, do not forget to put “squared” after each answer. Another way that you can write “squared is by putting a 2 at the top right of the last letter. Therefore, the answer to the last rec-tangle would look like this:

A =15 cmand the first rectangle would be written as

A = 2 cmThey both hold the same meaning, one is just faster and easier to write than the other.

Many students, again, question the purpose in learning how to find the area of shapes. Being able to find area will make other math equations that you will learn in the future much easier.

In the Widget on the next page, make sure to look through the pictures at the different forms that perimeter can be used.

5 cm

3 cm

5 cm

3 cm

2

2

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Learning to find the area of a rectangle is simple, however, if you are confused or would like to learn from someone your age, watch this video on finding area, a fourth grader made it!

There are many ways in which area takes place in everyday life. In order to put tile down on the kitchen floor, a carpenter must measure the area to know how many square units will fit in the kitchen. Also, if someone wants to plant a garden, they should measure the area of square units they have in order to know how many flowers and plants will fit.

Now that you have learned how to find the perimeter and area of a rectangle, take this review quiz to test your knowledge. If you find yourself still confused or getting the answers wrong, try going over the book a few more times to understand the con-cepts better.

INTERACTIVE 1.2 Area Youtube Video

A student provides information on how to find the area of a rectangle.

REVIEW 1.1 Quiz over Area and Perimeter

Check Answer

Question 7 of 7If I want to put a fence around the edges of my yard, I will measure the ______ of the yard.

A. Area

B. Perimeter

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Works Cited

Mathantics. “Math Antics - Perimeter.” Online video clip. Youtube.!! ! Youtube, 10 Feb 2014. Web. 23 April 2014.

VeryEasyLearning. “Area of Square, Rectangle, and Parallelogram - !! ! VERY EASY.” Online video clip. Youtube. Youtube, 16 Feb ! ! 2013. Web. 23 April 2014.

Book and Widget contains images found available under a Creative !! ! Commons Attribution-Noncommercial license.