This is the Grade 4 Mathematics Quarter 3 Module 8, Perimeter, a self-learning module (SLM) for home-based learning under the Alternative Delivery Mode. It was developed by DepEd Region V (First Edition, 2020). It teaches learners how to find the distance around a closed plane figure, starting from a simple idea: if you have walked around the outside of your house, you have already walked its perimeter.
After this module, learners should be able to find the perimeter of common shapes, both by measuring them and by using formulas, and to use perimeter to solve everyday problems such as fencing a lot or walking around a park.
On this page 7 sections
What learners will learn
After going through this module, learners are expected to:
- visualize the perimeter of any given plane figure in different situations;
- measure the perimeter of any given figure using appropriate tools; and
- find the perimeter of triangles, squares, rectangles, parallelograms, and trapezoids.
What perimeter means
The module defines perimeter as the distance around a closed plane figure. To find the perimeter of any polygon, add the measures of all its sides.
The lesson opens with a story problem. Narlito wants to build a fence around their rectangular lot, which has sides of 12 meters, 10 meters, 12 meters, and 10 meters. How long must the fence be? The module solves it in three steps:
- Picture the lot as a rectangle.
- Write a formula by adding the sides. A figure with 4 sides gives P = s + s + s + s.
- Put in the measurements and add: P = 12 m + 12 m + 10 m + 10 m = 44 m.
So Narlito needs 44 meters of fence.
Perimeter formulas in this module
The module shows shortcut formulas for some shapes, each with a worked example.
| Shape | Formula | Module example |
|---|---|---|
| Any polygon | Add all the sides | Trapezoid: 3 cm + 3 cm + 6 cm + 12 cm |
| Rectangle | P = 2 x (L + W) | 2 x (12 m + 10 m) = 2 x 22 m = 44 m |
| Square | P = 4 x s | 4 x 8 cm = 32 cm |
| Triangle | P = s + s + s | 11 cm + 11 cm + 14 cm = 36 cm |
The rectangle formula works because the opposite sides of a rectangle are equal. So the perimeter is 2 lengths plus 2 widths. A square has 4 equal sides, so you multiply one side by 4. The same idea applies to a parallelogram: the pretest uses 2 x (10 m + 8 m) for a parallelogram with sides of 10 m and 8 m.
Measuring real objects
The module also has learners measure the sides of a drawing with a measuring tool and then add them. It reminds them to choose the right tool and unit for the size of the object:
- Inches and centimeters for smaller objects
- Meters and feet for medium-sized spaces and objects
- Miles and kilometers for really long distances
Parts and activities of the module
- What I Know (pretest): choose the correct number sentence for the perimeter of five shapes, then find the perimeter of five more.
- What’s In: count the sides of a triangle, square, rectangle, trapezoid, and right triangle.
- What’s New: the story problem about Narlito’s fence.
- What is It: the explanation of perimeter and the formulas above.
- What’s More: find the perimeter of a square, two triangles, a rectangle, and a trapezoid.
- What I Have Learned: a short summary of the lesson.
- What I Can Do: Annabelle walks her dog around a rectangular park that is 22 m long and 17 m wide. How far does she walk?
- Assessment: find perimeters of figures, measure a picture frame and a window with a ruler, and complete a table for a square garden, a rectangular table, and a picture frame.
- Additional Activities: find the perimeters of a rectangle and the two triangles formed by its diagonal. Then measure the perimeter of a table at home and of one face of a box.
How to use this module
Learners: Start with the pretest to see what you already know. Then work 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 at the end of the module, and be honest when you check. Ask your teacher or facilitator if any part is hard.
Parents and facilitators: Help your child with the hands-on tasks. You will need a ruler or meterstick to measure a table at home and one face of a box. A quick talk about real perimeters, like the fence around your yard, can also help.
Teachers: The module covers finding the perimeter of a polygon by adding its sides and by using formulas for rectangles and squares. It also covers choosing measuring tools and units. The answer key covers the pretest, the activities, and the assessment. The measuring tasks at home have answers that may vary.
Frequently asked questions
What grade and quarter is this perimeter module for?
It is the Grade 4 Mathematics module for Quarter 3, Module 8. It was published by DepEd Region V as a first edition in 2020.
What is perimeter?
Perimeter is the distance around a closed plane figure. You find it by adding the measures of all the sides of the figure.
What is the formula for the perimeter of a rectangle and a square?
For a rectangle, P = 2 x (L + W), because opposite sides are equal. For a square, P = 4 x s, because all four sides are equal.
Does the module have an answer key?
Yes. The answer key at the end covers the pretest, What’s In, What’s More, What I Can Do, the assessment, and the additional activities. Measuring tasks done at home have answers that may vary.
Which shapes does the module cover?
It covers triangles, squares, rectangles, parallelograms, and trapezoids. It also includes measuring the perimeter of real objects like a table and a box.
Full text of the module
The text below is a transcription of the PDF above, as printed.
Mathematics Quarter 3 – Module 8: Perimeter
CO_Q3_Mathematics 4_Module 8
[illustration: group of learners and a teacher reading and studying outdoors and at a desk, with a globe and a lamp]
Mathematics– Grade 4 Alternative Delivery Mode Quarter 3 – Module 8: Perimeter First Edition, 2020
Republic Act 8293, section 176 states that: No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the government agency or office wherein the work is created shall be necessary for exploitation of such work for profit. Such agency or office may, among other things, impose as a condition the payment of royalties.
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
| Development Team of the Module | |
|---|---|
| Writer: | Michael L. Delgado |
| Editor: | Elena D. Hubilla |
| Reviewers: | Annavi M. Maravilla, Loyd H. Botor |
| Illustrator: | Michael L. Delgado |
| 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 |
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
4
Mathematics
Quarter 3 – Module 8: Perimeter
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
[illustration: target with an arrow, icon beside the part title]
Have you experienced walking around outside your house? If you have done this, you already have walked the distance of the house’s perimeter.
In this module, you will learn how to find the perimeter of a given figure. You can practically apply the things that you will learn from this module in your daily living.
After going through this module, you are expected to:
- visualize the perimeter of any given plane figure in different situations;
- measure the perimeter of any given figure using appropriate tools; and
- find the perimeter of triangles, squares, rectangles, parallelograms, and trapezoids.
What I Know
[illustration: pencil icon beside the part title]
A. Study the figure carefully. Choose the letter of the correct formula/number sentence for finding the perimeter of each polygon.
- [illustration: rectangle with sides labeled 10 m at top and bottom and 4 m at left and right]
a. 10 m + 10 m + 10 m +10 m = n b. 10 m + 10 m + 4 m + 4 m = n c. 10 m – 4 m + 10 m – 4 m = n d. 4 m + 4 m + 4 m +4 m = n
- [illustration: triangle with sides labeled 6 cm, 4 cm, and 8 cm]
a. 8 cm x 6 cm + 4 cm = n b. 8 cm – 6 cm + 4 cm = n c. 8 cm + 6 cm + 4 cm = n d. 8 cm – 6 cm x 4 cm = n
- [illustration: square with all sides labeled 3 m]
a. 3 m + 3 m + 3 m x 3m = n b. 3 m x 3 m = n c. 4 x 3 m = n d. 3 m x 3 m x 3m – 3m = n
- [illustration: trapezoid with top side 6 cm, slanted sides 3 cm and 3 cm, bottom side 12 cm]
a. 3 cm + 3 cm + 6 cm + 12 cm = n b. 3 cm x 3 cm + 6 cm + 12 cm = n c. 12 cm – 3 cm + 6 cm + 3 cm = n d. 3 cm + 3 cm + 6 cm – 12 cm = n
- [illustration: parallelogram with slanted sides 8 m and 8 m, top and bottom sides 10 m]
a. 10 m x 8 m = n b. 10 m + 8 m = n c. 2 x ( 10 m + 8 m) = n d. 8 m + 10 m – 8 m = n
B. Find the perimeter of each figure.
[illustration: rectangle with sides labeled 10 cm at top and bottom and 4 cm at left and right]
[illustration: isosceles triangle with sides labeled 4 m and 4 m and base 6 m]
[illustration: square with all sides labeled 3 cm]
[illustration: isosceles triangle with sides labeled 11 m and 11 m and base 15 m]
[illustration: trapezoid with top side 12 cm, slanted sides 2 cm and 2 cm, bottom side 14 cm]
If you are done answering the activity, please go to the Answer Key on page 15 and check if your answers are correct. Thank you for your honesty in answering and checking your work. Hope you will do this until the end of this module.
Lesson 1 Perimeter
What’s In
[illustration: puzzle pieces icon beside the part title]
Let us review first some of the concepts that can help you understand perimeter.
Examine closely the different polygons. Count the number of sides of each polygon and write the answer on the space provided.
- [illustration: triangle] _______
- [illustration: square] _______
- [illustration: rectangle] _______
- [illustration: trapezoid] _______
- [illustration: right triangle] _______
If you are done answering the activity, please go to the Answer Key on page 15 and check if your answers are correct. Thank you for your honesty in answering and checking your work. Hope you will do this until the end of this module.
What’s New
Let us start learning the new concept with the help of this story problem.
Read the story problem.
Narlito is planning to build a fence around their house. The shape of their lot is rectangular with the sides of 12 meters, 10 meters, 12 meters and 10 meters. What is the total length of the fence he needs to build?
[illustration: house with a fence, a brick wall, a window, a door, and a pile of sand]
What is asked in the problem?
What are the given facts that can help you solve the problem?
What can you say about Narlito?
Try to answer the problem. Have patience and have fun!
We will find out on the next part of this module whether you answered the problem properly and correctly.
What is It
To solve the given problem, we must find the distance around the lot of Narlito.
The distance around a closed plane figure is what we call perimeter. To determine the perimeter of the lot Narlito needs to fence, follow these steps:
- Visualize Narlitos’ lot.
[illustration: rectangle drawn on a dot grid, labeled 12 m on the top and bottom sides and 10 m on the left and right sides]
Derive the formula for the perimeter by adding the measure of each side of a given plane figure. Since the given figure has 4 sides, we say that Perimeter = side + side + side + side. Then, P = s + s + s + s
Using the formula you developed, substitute the measurement of each side then add.
So, P = s + s + s + s P = 12 m + 12 m + 10 m + 10 m P = 44 m
Therefore, the perimeter of Narlitos’ lot is 44 meters. Thus, Narlito needs to fence 44 m.
Can you think of other ways to find the length of the fence he needs to build?
Let us try to visualize Narlitos’ lot.
[illustration: rectangle drawn on a dot grid, labeled 12 m on the top and bottom sides and 10 m on the left and right sides]
Let L be the length and W be the width of the rectangle.
Since the opposite parallel sides of a rectangle are equal in lengths, we say that Perimeter = 2 x L + 2 x W or Perimeter = 2 (Length + Width).
Then, Perimeter of a rectangle = 2 (L + W)
Using the formula you developed, substitute the measurement of each side then compute.
So, P = 2 (L x W) P = 2 (12m + 10m) P = 2 (22m) P = 44 m
Therefore, the perimeter of Narlitos’ lot is 44 meters.
Thus, Narlito needs to fence 44 m.
What if Narlito has a square lot? How do we solve its perimeter?
Let us try to solve for the perimeter of a square using this example.
[illustration: square with each side labeled 8cm]
A square has 4 equal sides. We can find its perimeter by following these steps:
- Aside from adding the 4 sides we can derive a formula for the perimeter of a square. Since the given figure has 4 equal sides, we say that Perimeter = 4 x side.
Then, Perimeter of a square = 4 x s
- Using the formula you developed, substitute the measurement of each side then add.
So, P = 4 x s P = 4 x 8cm P = 32cm
Therefore, the perimeter of the square is 32cm.
But what if you will be solving for the perimeter of a triangle? How do we solve for its perimeter?
Let us try to solve for the perimeter of a triangle using this example.
[illustration: triangle with two sides labeled 11 cm and the base labeled 14 cm]
A triangle has 3 sides. We can find its perimeter by following these steps:
Derive the formula for the perimeter by adding the measure of each side of a given plane figure. Since the given figure has 3 sides, we say that Perimeter = side + side + side (P = s + s + s)
Add the measures of all its sides.
So, P = 11 cm + 11 cm + 14 cm P = 36 m
Therefore, the perimeter of the given triangle is 36 cm.
You may follow the given steps in solving for the perimeter of other plane figures.
Just always remember that the perimeter is the total distance around a closed plane figure.
Let us now try measuring perimeter using an appropriate tool by performing the given task below.
Use an appropriate measuring tool to find the perimeter of the picture shown. Put the measurements in the box provided.
[illustration: computer monitor drawing with three empty measurement boxes, one above the screen and one on each side of the monitor]
What are the measures of each side? What is the perimeter?
What measuring tool did you use? Why?
What unit did you use for the perimeter? Why?
Always remember that when measuring the perimeter of real objects, you need to use the appropriate tool and unit of length for the object.
- Inches and centimeters are used for smaller objects.
- Meters and feet are used for medium sized spaces and objects.
- Miles and kilometers are used for really long distances.
What’s More
Let us see if you already know how to find the perimeter of closed plane figures.
Find the perimeter of each figure.
- [illustration: square with all sides labeled 5 cm]
- [illustration: triangle with two sides labeled 9 m and the base labeled 10 m]
- [illustration: rectangle with top and bottom labeled 16 cm and sides labeled 8 cm]
- [illustration: triangle with two sides labeled 7 m and the base labeled 8 m]
- [illustration: trapezoid with top labeled 13 cm, slanted sides labeled 6 cm, and bottom labeled 17 cm]
If you are done answering the activity, please go to the Answer Key on page 15 and check if your answers are correct. Thank you for your honesty in answering and checking your work. Hope you will do this until the end of this module.
What I Have Learned
You are doing great! Just always remember:
The perimeter of a closed figure is the distance around the figure.
To find the perimeter of a polygon:
- get the sum of the measurements of its sides.
What I Can Do
Let us see if you are now ready to solve this problem.
Read and understand the problem, then answer the questions that follow.
[illustration: Annabelle walking with her dog around a rectangular park lined with lamp posts]
Annabelle, together with her dog walks around the rectangular park every day to stay fit. If the park has a length of 22 m and a width of 17 m, what is the distance that Annabelle walks?
What can you say about Annabelle?
What is asked in the problem?
What are the given facts that can help you solve the problem?
Solve for the distance that Annabelle walks. What is the answer?
Assessment
You are now ready for the next activity.
A. Find the perimeter of each figure.
- [illustration: rectangle with top and bottom labeled 15 cm and sides labeled 7 cm]
- [illustration: triangle with two sides labeled 8 m and the base labeled 10 m]
- [illustration: square with all sides labeled 8 cm, bottom labeled 8 m]
- [illustration: triangle with two sides labeled 17 m and the base labeled 23 m]
- [illustration: trapezoid with top labeled 24 cm, slanted sides labeled 9 cm, and bottom labeled 27 cm]
B. For numbers 6 and 7, follow the following steps:
a. Use a ruler to measure the sides of each figure in centimeters. b. Write each length in the blank. c. Compute for the perimeter.
_____ cm
_____ cm _____ cm P = _____ cm
_____ cm
[illustration: picture frame with a tree, a sun, and hills inside]
_____ cm
_____ cm _____ cm P = _____ cm
_____ cm
[illustration: window with two curtains]
C. Complete the table.
| Figure | Length | Width | Perimeter |
|---|---|---|---|
| 8. A square garden | 12 m | ||
| 9. A rectangular table | 5 m | 2 m | |
| 10. Picture frame | 16 cm | 12 cm |
Additional Activities
Let us try some more.
A. Find the perimeter in meters.
[chart: diagram of rectangle ABCD with diagonal from B to C; labels as printed]
- A (top-left corner), 60 m (top side, from A to B), B (top-right corner)
- 25 m (left side)
- 65 cm (diagonal, from C to B)
- C (bottom-left corner), D (bottom-right corner)
Rectangle ABCD = ________ m Triangle ABC = ________ m Triangle BCD = ________ m
C. Do what is asked.
- Use a meterstick or a ruler to measure the perimeter of your table at home.
- Use a ruler to measure the perimeter of one face of a box.
If you are done answering the activity, please go to the Answer Key on page 15 and check if your answers are correct. Thank you for your honesty in answering and checking your work. Congratulations!
transcriber’s note: this page is printed upside down; it is transcribed upright below.
Answer Key
What I Know
A.
- b
- c
- c
- a
- c
B.
- P= 28 cm
- P= 14 m
- P= 12 cm
- P= 37 m
- P= 30 cm
What’s In
- 3
- 4
- 4
- 4
- 3
What’s More
- P= 20 cm
- P= 28 m
- P= 48 cm
- P= 22 m
- P= 42 cm
What I Can Do
- She is health conscious.
- The distance that Annabelle walks
- length of 22m and width of 17m
- P= 78 m
Assessment
A.
- P= 44 cm
- P= 26 m
- P= 32 cm
- P= 57 m
- P= 69 cm
B.
[illustration: rectangle with sides labeled 5 cm (top), 3 cm (left), 5 cm (bottom), 3 cm (right); P = 16 cm]
[illustration: square-shaped window with sides labeled 6 cm on each side; P = 24 cm]
C.
| Figure | Length | Width | Perimeter |
|---|---|---|---|
| 8. A square garden | 12 m | 12 m | 48 m |
| 9. A rectangular table | 5 m | 2 m | 14 m |
| 10. Picture frame | 16 cm | 12 cm | 56 cm |
Additional Activities (pages 13)
A.
- Rectangle ABCD= 170 m
- Triangle ABC= 150 m
- Triangle BCD= 150 m
B.
- Answers may vary.
- Answers may vary.
References
K to 12 Mathematics Curriculum Guide, August 2016
Tabilang, Alma R. et al. Mathematics 4 Learner’s Material. Department of Education. 2015.
Tabilang, Alma R. et al. Mathematics 4 Teacher’s Guide. Department of Education. 2015.
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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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