This is the Grade 4 Mathematics self-learning module for Quarter 3, Module 10: “Differentiating Perimeter from Area.” It was developed by DepEd Region V for home-based learning, and it has one lesson. After working through it, learners should be able to tell perimeter and area apart and find both for squares and rectangles.
On this page 6 sections
What learners will learn
The module states one learning goal:
- Differentiate perimeter from area.
Along the way, learners also practice:
- Finding perimeter by counting linear units along the outline of a figure.
- Finding area by counting square units inside a figure.
- Using shortcuts for squares and rectangles.
- Deciding whether a real-life task needs perimeter or area.
Perimeter and area: the key ideas
The meaning of each term
- Perimeter is the distance around a closed figure. If the figure has straight sides, the perimeter is the sum of the lengths of all its sides. The word can also mean the outline or border itself.
- Area is the amount of surface a closed figure encloses, that is, the space inside the outline.
The garden example
The lesson opens with Teacher Pat. She needs carpet grass to cover a rectangular school garden that is 6 meters long and 4 meters wide. She also needs fencing to go around it. Her helper, Criselda, cannot tell perimeter from area, so the module walks through both on a grid.
- Fence (perimeter): There are 20 linear units along the outline, so the perimeter is 20 meters. The shortcut is twice the length plus twice the width: 12 m + 8 m = 20 m.
- Grass (area): There are 24 square units inside the rectangle, so the area is 24 square meters. The shortcut is length times width: 6 m x 4 m = 24 square meters.
Teacher Pat needs 20 meters of fence and 24 square meters of carpet grass.
Formulas for squares and rectangles
The module compares a square with 4 cm sides and a rectangle 7 cm long and 3 cm wide.
| Figure | Perimeter | Area |
|---|---|---|
| Square (side 4 cm) | 4 x side = 16 cm | side x side = 16 square cm |
| Rectangle (7 cm by 3 cm) | 2 x length + 2 x width = 20 cm | length x width = 21 square cm |
The perimeter of a square is 4 times one side, because all four sides are equal. The perimeter of a rectangle is twice the length plus twice the width, because its opposite sides are equal.
How perimeter and area differ
| Basis | Perimeter | Area |
|---|---|---|
| Meaning | Distance around a closed figure | Amount of surface enclosed in a closed figure |
| Unit of measurement | Linear units (for example, meters) | Square units (for example, square meters) |
| Number of dimensions | One | Two |
| Example | Length of fence needed to enclose a garden | Square units of grass needed to cover a garden |
The pretest also points out that there is no fixed relationship between the two numbers. A figure’s perimeter in linear units can be less than, equal to, or greater than its area in square units.
The practice task uses everyday situations. Building a fence around an orchard or putting lace around a neckerchief is about perimeter. Covering a floor with tiles or painting a whole wall is about area.
Parts of the module
- What I Need to Know: the lesson goal.
- What I Know: a 10-item multiple-choice pretest.
- What’s In: a review that matches side, length, and width to their meanings, then finds the perimeter of a square and a rectangle.
- What’s New: Teacher Pat’s garden problem.
- What is It: the discussion of perimeter and area.
- What’s More: a table to fill in that compares perimeter and area.
- What I Have Learned: a summary of the differences.
- What I Can Do: six real-life statements to label A (area) or P (perimeter).
- Assessment: four multiple-choice items, plus counting the area and perimeter of three grid figures.
- Additional Activities: drawing an 11-unit square and a rectangle on graphing paper, finding their perimeter and area, and writing how a square’s side relates to its perimeter and area.
- Answer Key: answers for the tests and activities.
How to use this module
For learners: Start with the pretest to see what you already know. Then go through the parts in order. Write your answers on a separate sheet of paper, not on the module. Check your work with the answer key only after you finish each part, and be honest when you use it. If something is hard to understand, ask your teacher or facilitator.
For parents: Help your child count squares and border units on the grids. Ordinary tasks at home also work well for practice, like measuring around a table or counting the floor tiles in a room.
For teachers: The answer key is printed at the end of the module, even though the activities point to page 14. Please check a few printed answers before learners rely on them:
- What’s In, items 4 and 5: By the module’s own formulas, the perimeters are 20 cm (a square with 5 cm sides) and 24 cm (a 5 cm by 7 cm rectangle). The key says 28 m and 30 m.
- Assessment, item 3: By the module’s own summary, perimeter has one dimension and area has two, which is choice d. The key says b.
The table in “What is It” also gives the areas as 16 cm and 21 cm. These should be read as square centimeters.
Frequently asked questions
What grade and quarter is this perimeter and area module for?
It is the Grade 4 Mathematics self-learning module for Quarter 3, Module 10. It has one lesson, “Differentiating Perimeter from Area.”
What is the difference between perimeter and area?
Perimeter is the distance around a closed figure and is measured in linear units. Area is the amount of surface inside the figure and is measured in square units. Perimeter involves one dimension, while area involves two.
How do you find the perimeter and area of a rectangle?
Perimeter is twice the length plus twice the width. Area is length times width. For a 6 m by 4 m garden, the perimeter is 20 meters and the area is 24 square meters.
How do you find the perimeter and area of a square?
Perimeter is 4 times the length of one side. Area is the side multiplied by itself. A square with 11-unit sides has a perimeter of 44 units and an area of 121 square units.
Does the module have an answer key?
Yes. The answer key at the end covers the pretest, the review, the activities, and the assessment. A few printed answers should be double-checked: What’s In items 4 and 5, and Assessment item 3.
Full text of the module
The text below is a transcription of the PDF above, as printed.
Mathematics Quarter 3 – Module 10: Differentiating Perimeter from Area
4
[illustration: cover art of students learning outdoors and at home, with a teacher, a globe, and a student reading by lamplight]
CO_Q3_Mathematics 4_Module 10
Mathematics – Grade 4 Alternative Delivery Mode Quarter 3 – Module 10: Differentiating Perimeter from Area First Edition, 2020
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Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names, trademarks, etc.) included in this module are owned by their respective copyright holders. Every effort has been exerted to locate and seek permission to use these materials from their respective copyright owners. The publisher and authors do not represent nor claim ownership over them.
Published by the Department of Education Secretary: Leonor Magtolis Briones Undersecretary: Diosdado M. San Antonio
Printed in the Philippines by ________________________
Department of Education – Region V
Office Address : Regional Center Site, Rawis, Legazpi City, 4500 Telefax : 0917-178-1288 E-mail Address : region5@deped.gov.ph
Development Team of the Module
Writer: Nancy D. Fara-on Editor: Elena D. Hubilla Reviewer: Loyd Botor Illustrator: Ireneo D. Dechavez Layout Artist: Cherry Lou O. Calison Management Team: Gilbert T. Sadsad, Francisco B. Bulalacao Jr., Grace U. Rabelas, Ma Leilani R. Lorico, Monserat D. Guemo, Florena M. Deuna
Mathematics
Quarter 3 – Module 10: Differentiating Perimeter from Area
4
Introductory Message
This Self-Learning Module (SLM) is prepared so that you, our dear learners, can continue your studies and learn while at home. Activities, questions, directions, exercises, and discussions are carefully stated for you to understand each lesson.
Each SLM is composed of different parts. Each part shall guide you step-by-step as you discover and understand the lesson prepared for you.
Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will tell you if you need to proceed on completing this module or if you need to ask your facilitator or your teacher’s assistance for better understanding of the lesson. At the end of each module, you need to answer the post-test to self-check your learning. Answer keys are provided for each activity and test. We trust that you will be honest in using these.
In addition to the material in the main text, Notes to the Teacher are also provided to our facilitators and parents for strategies and reminders on how they can best help you on your home-based learning.
Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use a separate sheet of paper in answering the exercises and tests. And read the instructions carefully before performing each task.
If you have any questions in using this SLM or any difficulty in answering the tasks in this module, do not hesitate to consult your teacher or facilitator.
Thank you.
What I Need to Know
Area and perimeter are two important concepts in mathematics. Both have practical applications and are used in our day-to-day lives. Perimeter is the distance around a figure while area is the measure of the surface enclosed within a region.
Different shapes may have the same perimeter but different areas, or they may have the same area but different perimeters. Still, there are different shapes having the same area and perimeter.
At the end of this module, you should be able to differentiate perimeter from area.
What I Know
Read and answer each item carefully. Choose the letter of the correct answer.
For a closed figure, what do we look at when we want to know its area?
a. outside the closed figure
b. its outline
c. inside the closed figure
d. either outside or inside the closed figureIf you have to build a fence around your backyard, what will you measure to find the amount of fencing material you would need?
a. side b. perimeter c. area d. volumeFor a closed figure, what do we look at when we want to know its perimeter?
a. its corners
b. its outline
c. its inside/surface
d. either outside or inside the closed figureMang Ramon wants to surround his rectangular flower garden with a wooden fence. What does he need to measure to find how much wooden fence he needs?
a. area c. perimeter
b. volume d. sideWhich of the following statements best describes the relation between the number of linear units along the outline of a figure and the number of square units enclosed in its outline?
a. They are the same.
b. The number of linear units is greater than the number of square units
c. The number of linear units is less than the number of square units.
d. There is no relation as the number of linear units along the outline of a figure may be less than, equal to, or greater than the number of square units enclosed within the outline of the figure.The shape shown has an area of 35 square units. What is its perimeter?
a. 30 units
b. 20 units
c. 25 units
d. 24 units
[illustration: grid of unit squares forming a figure with an area of 35 square units]
- What is the area of a square with a perimeter of 20 units?
a. 20 sq units
b. 25 sq units
c. 30 sq units
d. 35 sq units
[illustration: grid of unit squares forming a square]
- What is the area of a square with a perimeter of 24 units?
a. 34 square units
b. 35 square units
c. 32 square units
d. 36 square units
[illustration: grid of unit squares forming a square]
- The shape shown has an area of 48 square units. What is its perimeter?
a. 26 units
b. 28 units
c. 30 units
d. 36 units
[illustration: grid of unit squares forming a rectangle with an area of 48 square units]
- What is the perimeter of the rectangle below which has an area of 60 square meters?
a. 38 meters
b. 40 meters
c. 36 meters
d. 42 meters
[illustration: grid of unit squares forming a rectangle with an area of 60 square meters]
Are you done answering? If yes, time to check. Please go to page 14 for the Answer Key.
Lesson 1: Differentiating Perimeter from Area
What’s In
A. Matching type: Match the terms in Column A with their descriptions in column B. Choose the letter of the correct answer.
| A | B |
|---|---|
| _______1. side | a. the longer side of a rectangle |
| _______2. length | b. a line that is part of the outline of a geometric figure |
| _______3. width | c. the shorter side of a rectangle |
B. Find the perimeter of each figure. Use the formula.
[illustration: square with each side labeled 5 cm]
[illustration: rectangle with a side labeled 5 cm and the adjacent side labeled 7 cm]
Are you done answering? If yes, time to check. Please go to page 14 for the Answer Key.
What’s New
Teacher Pat wants to know how many square meters of carpet grass will be needed to cover the 6 meters by 4 meters rectangular garden in the school yard and the exact length of fencing materials needed to enclose it. She doesn’t want to waste money by ordering more than the materials needed or by ordering too little. She asked Criselda to find the area and the perimeter of the garden. But the problem is, she cannot differentiate perimeter from area.
Below is an illustration of the rectangular garden. Let us help Teacher Pat solve the problem.
[illustration: rectangular garden drawn with plants and shrubs; labeled “4 meters” along the vertical side and “6 meters” along the bottom side]
What is It
Before we continue with the discussion, let us first understand the meaning of perimeter and area of a certain shape or plane figure.
Perimeter is the distance around a closed figure. If the figure is formed by straight lines, the perimeter is the sum of all the lengths of these lines. The straight lines are referred to as the sides of the figure.
Area is the measure of the region or surface a figure encloses.
To better understand these two concepts and their difference, let’s use the figure below.
[chart: grid sheet representation of a rectangle; labels as printed: “Width – 4” (vertical side) and “Length – 6 meters” (bottom side); shaded interior region shown inside the outlined rectangle]
The figure is a graph/grid sheet representation of the rectangular garden measuring 6 meters by 4 meters.
The outline or border is where Teacher Pat is to put the fence. The shaded portion is the part of the garden that needs to be covered with carpet grass.
The whole length of the outline or the border is the perimeter of the rectangular garden and is also the length of the fence Teacher Pat needs to enclose the garden.
To find its perimeter, count the number of linear units along the border or outline of the rectangle. Clearly, there are 20 linear units along the outline of the rectangle. Therefore, the perimeter of the rectangular garden is 20 units or 20 meters.
Observe that we could have gotten the perimeter of the rectangular garden by adding twice the length and twice the width. Twice 6 meters is 12 meters; and twice 4 meters is 8 meters. The sum is, of course, 20 meters.
While we have used the term perimeter here to refer to the distance around the closed figure, it may also be used to refer to the outline or the border of the closed figure.
The area of this rectangular garden, on the other hand, is the amount of surface enclosed within the rectangle. For Teacher Pat, this is what needs to be covered with carpet grass.
To find the area of the garden, count the number of square units enclosed within the rectangle. We can count 24 square units enclosed within the rectangle. Therefore, the area of the rectangular garden is 24 square units, or 24 square meters.
Observe that we could have gotten the area of the rectangular garden by multiplying its length and width. The product of 6 meters and 4 meters is, of course, 24 square meters.
Teacher Pat therefore needs 20 meters of fence to enclose the garden and 24 square meters of carpet grass to cover it.
Let us look at the square and the rectangle below as we try to observe how their perimeters and areas relate to the length of their sides.
[chart: grid sheet representations of a square and a rectangle; labels as printed: “Side – 4 cm” (square), “Width – 3 cm” and “Length – 7 cm” (rectangle)]
The table below shows us the lengths of the sides of the figures and their perimeter and areas.
| Figure | Side | Length | Width | Perimeter | Area |
|---|---|---|---|---|---|
| Square | 4 cm | – | – | 16 cm | 16 cm |
| Rectangle | – | 7 cm | 3 cm | 20 cm | 21 cm |
Observe that:
For the square: The perimeter is 4 times the length of one side. This is because all its four sides are of the same length. The area, on the other hand, is the square of the length of one side.
For the rectangle, the perimeter is the sum of twice its length and twice its width. This is because the two pairs of opposite sides have the same length. The area, on the other hand, is the product of the length and width.
Are the above observations true for all squares and rectangles? Why?
What’s More
Differentiate perimeter from area by filling-in the table below using the different phrases and statements that follow.
| Basis | Area | Perimeter |
|---|---|---|
| Meaning | 1. | 2. |
| Unit of measurement | 3. | 4. |
| No. of dimensions | 5. | 6. |
| Example | 7. | 8. |
a. Amount of surface enclosed within a closed figure. b. Square units c. Linear units d. Distance around a closed figure e. One f. Two g. The number of square units of grass to cover a garden h. Length of fence required to enclose a garden.
Are you done answering? If yes, time to check. Please go to page 14 for the Answer Key.
What I Have Learned
The differences between perimeter and area are:
- Perimeter is the distance around a closed figure or the length of the outline of a closed figure. Area is the measurement of the amount of surface enclosed within the closed figure.
- Perimeter is expressed in linear units; area in square units
- Perimeter involves only one dimension; area involves two dimensions.
What I Can Do
Write A if the statement talks about area and P if it talks about perimeter.
Aling Juana wants to build a fence around her lemon orchard.
Mang Mario covered his living room with wooden tiles.
Rissa wants to put some lace around the edges of her neckerchief.
The interior decorator painted the entire wall in his favorite color.
Darrel surrounded the flower garden with bamboo sticks.
She covered the stain on the table with a fresh coat of paint.
Are you done answering? If yes, time to check. Please go to page 14 for the Answer Key.
Assessment
Read each item carefully. Choose the letter of the correct answer.
Which of the following statements best describes the difference between perimeter and area?
a. Area is the measurement of the surface enclosed within a closed figure while perimeter is the distance around the closed figure.
b. Area is the distance around a closed figure while perimeter is the measure of the surface enclosed within the closed figure.
c. Area is measured by counting the linear units along the outline of a closed figure while perimeter is measured by counting the number of square units enclosed in the figure.
d. Area and perimeter have the same measurement.How does area differ from perimeter when it comes to measurement?
a. Measurement of perimeter is expressed in square units while area is expressed in linear units.
b. Measurement of area is expressed in square units while perimeter is expressed in linear units.
c. Area, in terms of the number of square units, is always less than perimeter, in terms of linear units.
d. Area, in terms of the number of square units, is always equal to perimeter, in terms of the number of linear units.How does area differ from perimeter when it comes to dimensions?
a. Perimeter has two dimensions while area has only one dimension.
b. Both perimeter and area have two dimensions.
c. Perimeter has two dimensions while area has no dimensions.
d. Perimeter has only one dimension while area has two dimensions.Which of the following statements uses the measurement of both area and perimeter?
a. the capacity of a box and the length of a table.
b. the length of the stage and the width of the classroom.
c. space amount of surface covered by the garden and the length of fence required to enclose the garden.
d. the height of the building and the length of the door.
Find the area and the perimeter of the following figures by counting the corresponding units.
1 linear unit — 1 square unit –
[illustration: two grids of unit squares, one at the top left and one at the top right, each showing a rectangular arrangement of squares to be counted]
- Area _________ 7. Area __________
- Perimeter _________ 8. Perimeter __________
[illustration: a long, three-row grid of unit squares to be counted]
- Area _________
- Perimeter _________
Are you done answering? If yes, time to check. Please go to page 14 for the Answer Key.
Additional Activities
Using a graphing paper,
- Draw a square which is 11 units on each side and showing the number of square units enclosed.
- Determine the perimeter by counting the linear units along the outline of the square; and the area by counting the square units enclosed within the outline of the square.
- Draw any rectangle and indicate its length and width.
- Determine the perimeter and the area of your rectangle by counting the linear units along its outline and the square units within the outline of the rectangle.
- Write the relationship between the length of a square and its perimeter and also its area.
Are you done answering? If yes, time to check. Please go to page 14 for the Answer Key.
Answer Key
What I Can Do
- P
- A
- P
- A
- P
- A
Assessment
- a
- b
- b
- c
- 72 sq m
- 34 m
- 63 sq m
- 32 m
- 75 sq m
- 56 m
Additional Activities
- [illustration: drawing of a square that has 11 units on each side]
- Area = 121 sq units; Perimeter = 44 units
3-4. (answers may vary) - The perimeter of a square is four times the length of a side of the square. The area of a square is the length of a side of the square multiplied by itself.
| Basis for Comparison | Perimeter | Area |
|---|---|---|
| Meaning | Distance around a closed figure. | Amount of surface enclosed in a closed figure. |
| Unit of measurement | Linear unit | Square units |
| No. of dimensions | One | Two |
| Example | Length of fence required to enclose the garden. | The number of square units of grass to cover a garden. |
What I Know
- c
- b
- b
- c
- d
- d
- b
- d
- b
- a
What’s In
- b
- a
- c
- 28 m
- 30 m
References
Book
Tabilang, Alma R. et. Al. Mathematics 4 Learner’s Material. Department of Education. 2015. pp. 188-191,
Website
Surbhi S. “Difference Between Area and Perimeter.” Keydifference.Com. . September 1, 2017. https://keydifferences.com/difference/between-area-and-perimeter.html
For inquiries or feedback, please write or call:
Department of Education – Bureau of Learning Resources (DepEd-BLR)
Ground Floor, Bonifacio Bldg., DepEd Complex Meralco Avenue, Pasig City, Philippines 1600
Telefax: (632) 8634-1072; 8634-1054; 8631-4985
Email Address: blr.lrqad@deped.gov.ph * blr.lrpd@deped.gov.ph
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