This module teaches students how to find the area of irregular figures by partitioning them into rectangles and squares. It provides examples of breaking down irregular figures and calculating the total area by adding the individual areas of the partitions. Students learn to cut figures with horizontal and vertical lines and label each part to find their lengths and widths. Practice problems are included for students to find the areas of different irregular shapes.
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2. Mathematics – Grade 4
Alternative Delivery Mode
Quarter 4 – Module 1: Finding the Areas of Irregular Figures
First Edition, 2020
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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
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Writer: Nancy D. Fara-on
Editor: Elena D. Hubilla
Reviewer: Loyd H. Botor
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Layout Artist: Cherry Lou O. Calison
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3. 1
CO_Q4_Mathematics4_ Module1
What I Need to Know
It may seem easy to find the area of a plane figure like a
rectangle or a square, but what if the figure has more than four
sides or if it is irregular?
In this module, you will understand how to partition an
irregular figure into squares and/or rectangles to find the area of
the irregular figure.
After going through this module, you are expected to find the
area of irregular figures made up of squares and rectangles using
sq. cm and sq. m.
What I Know
Analyze each diagram below and answer the questions that follow.
For questions 1 to 3, consider the figure below.
3 cm
6 cm
1. What is the area of square A?
2. What is the area of rectangle B?
3. What is the total area of figures A and B?
For questions 4 to 6, consider the figure below. Rectangle A is 8
cm long and 4 cm wide. Rectangle B is 6 cm long and 5 cm wide.
8 cm
A
B
3 cm
cm
3
4. 2
CO_Q4_Mathematics4_ Module1
4. What is the area of rectangle A?
5. What is the area of rectangle B?
6. What is the total area of rectangles A and B?
Find the area of each irregular figure.
In each figure, identical markings are used to show that the sides
are of equal length (congruent). Sides with the same number of
markings are equal in length.
8)
7) 1 cm
3 cm
5 cm
2 cm
4 cm
9. 10.
2 m
3 m
1 m 6 m
CONGRATULATIONS! If you got a score of 9 or 10, you
should not have any difficulty studying the lesson in this
module.
If you got a score of 8 or below, you may need to study the
lesson more carefully and do all the given activities.
cm
2
4 cm
cm
4
2 cm
1 cm
m
2
m
2
5. 3
CO_Q4_Mathematics4_ Module1
a. 16 cm2
10 cm
m
12 b. 36 cm2
e. 120 cm2
cm
8 f. 144 m2
5.
12 m
To find the area of
a square, we use
the formula:
A = s x s
For the rectangle,
we use the
formula: A = l x w
.
Lesson
1 Finding the Areas of Irregular Figures
What’s In
Let’s do this activity for a quick recall of finding the area of a
square or a rectangle.
Match the square or rectangle in Column A to its area in Column
B. Write the letter of the correct answer on your answer sheet.
Column A Column B
1.
2.
7 m
c. 84 m2
3. 6 cm
d. 100 cm2
4. 2 cm
6. 4
CO_Q4_Mathematics4_ Module1
What is It
Let’s take a look at the shape of their garden. How can you break
it up into rectangles and/or squares?
4 m
3 m
12 m
Let’s find the area of the irregular figure following these steps.
Solution A. Using a Horizontal Cut
a. Draw a horizontal line to form a rectangle and a square.
The illustration below shows how it is done.
Two figures are formed: square X and rectangle Y.
4 m
3 m
12 m
b. Find the areas of the square and the rectangle.
Area of the square X
A = s x s
= 4 m x 4 m
= 16 m2
Area of the rectangle Y
A = L x W
= 12 m x 3 m
= 36 m2
m
4
m
4
m
4
m
4 X
m
4
Y
7. 5
CO_Q4_Mathematics4_ Module1
c. Get the area of the irregular figure by adding the areas of the
square and the rectangle.
Total area of the irregular figure = area of X + area of Y
= 16 m2 + 36 m2
= 52 m2
Therefore, the total area of their garden is 52 m2
.
Solution B: Using Vertical Cuts
a. Let’s cut up the figure into three rectangles using vertical lines.
We have rectangle X, rectangle Y and rectangle Z.
4 m 4 m
12 m 4 m 4 m 4 m
b. Find the lengths and widths of the rectangles and solve for the
area of each.
Area of rectangle
X
Area of rectangle Y
A = L x W
A = L x W = 7 m x 4 m
2
= 4 m x 3 m How did we = 28 m
= 12 m
2
get 7 m?
We added 4
m and 3 m.
8. 6
CO_Q4_Mathematics4_ Module1
Area of rectangle Z
A = L x W
= 4 m x 3 m
= 12 m2
c. Then, add the areas of the three rectangles to get the area of the
irregular figure.
Area of the irregular figure = X + Y + Z
= 12 m2 + 28 m2 + 12 m2
= 52 m2
Therefore, the total area of their garden is 52 m2
.
Let’s try other examples.
1.
2m
4 m 3 m
7 m
For the irregular figure above, how do you cut up the figure
into rectangles and/or squares?
Consider this.
2m
4 m 3 m
7 m
Two rectangles are formed: rectangle X and rectangle Y.
X
5 m
Y
9. 7
CO_Q4_Mathematics4_ Module1
Area of rectangle X
A = l x w
Area of rectangle Y
A = l x w
= 2 m x 4 m = 5 m x 3 m
= 8 m2
How did we = 15 m2
get 5 m?
We subtracted
2 m from 7 m.
The sum of the areas of rectangles X and Y gives
the area of the irregular figure.
Area = X + Y
= 8 m2 + 15 m2
= 23 m2
The area of the given irregular figure
is 23 m2
.
How can you break it up into
rectangles and/or
squares?
The rectangle formed is
labelled X and the two squares
formed are labelled Y and Z. Area of square Y
6 cm
A = s x s
= 2 cm x 2 cm
= 4 cm2
How did we get 2 cm?
A = l x w
We
subtracted
2 cm from
2 cm 2 cm Area of square Z
A = s x s
= 2 cm x 2 cm
= 4 cm2
.
2 6 cm
4 cm
4 cm
2 cm 2 cm
cm
4
x
Y Z
4 cm
10. 8
CO_Q4_Mathematics4_ Module1
Area of rectangle X
4 = 6 cm x 2 cm cm which is the original = 12 cm2
length.
Area of the irregular figure
= area of X + area of Y + area of Z
= 12 cm2 + 4 cm2 + 4 cm2
= 20 cm2
The area of the given irregular figure is 20 cm2
.
What’s More
Let’s have some practice.
Find the area of each irregular figure.
1 2.
8 m
9 cm
6 cm
10 m
Let us summarize what you have learned:
cm
8
cm
2
cm
3
cm
6
8 m
10 m
11. 9
CO_Q4_Mathematics4_ Module1
To find the area of an irregular figure that is made up of
squares and rectangles:
• First, break or cut the figure into squares and/or rectangles.
• Next, find the area of each square and/or rectangle.
• Then, add the areas of the squares and/or rectangles.
What I Can Do
Mr. Delgado is going to plant frog grass in their front yard as
shown in the diagram. What is the area of the front yard that will
be planted with frog grass?
Find the area of each irregular figure.
1. 2.
12 m
5 cm
Assessment
.
15 m
20 m
6 m
What I Have Learned
12. 10
CO_Q4_Mathematics4_ Module1
9 m
3. 4.
4 m 4
m
8 m 10 m 6m
3 m
5. 6.
5 cm 5 cm
1 cm
8 cm 4cm
7. 8.
18 m
6 m
2 m
3 m
8 m
2 m
cm
15
11 cm
cm
1
m
14
m
4
3 cm
5 cm
10 cm
13. 11
CO_Q4_Mathematics4_ Module1
9. 10.
Mr. De la Cruz constructed an infinity pool which measures
15 meters long and 6 meters wide. He decided to attach to its
shorter side, a square pool with a side of 4 meters. Find the area
occupied by the entire pool.
Are you done answering?
If yes, time to check. Please go to page 14 for the Answer Key.
15. 13
CO_Q4_Mathematics4_ Module1
References
DepEd Order No. 12, s. 2020.Adoption of the Basic Education
Learning Continuity Plan for SY 2020-2021 In Light of the Covid-19
Public Health Emergency. June 19, 2020. p. 342.
Tabilang, Alma R., Arce, Ian Jay B., Pascua, Rodrigo V., Calayag, Nelma
P., Dacubo, Lolita p., Borais, Diolata B., Buemia, Rafael B., collao, Myra
T., Morandante, Larry G., Danao, Amado B., Gonzaga, Laura N., Briones,
Isagani A., Daganta,
John Antonio D., 2015, Mathematics 4 Learner’s Material, Department
of Education
Tabilang, Alma R., Arce, Ian Jay B., Pascua, Rodrigo V., Calayag, Nelma
P., Dacubo, Lolita p., Borais, Diolata B., Buemia, Rafael B., collao, Myra
T., Morandante, Larry G., Danao, Amado B., Gonzaga, Laura N., Briones,
Isagani A., Daganta, John Antonio D., 2015, Mathematics 4 Teacher’s
Guide, Department of Education.
.ph
16. 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. Bh.lrad@deped.gov.ph*bh.lrpd@deped.gov.ph
