5
Mathematics
Fourth Quarter
Module 1: Finding the Area of
a Given Circle
Republic of the Philippines
Department of Education
REGION VII-CENTRAL VISAYAS
SCHOOLS DIVISION OF SIQUIJOR
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OIC-Schools Division Superintendent: Dr. Neri C. Ojastro
Assistant Schools Division Superintendent: Dr. Edmark Ian L. Cabio
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E Edesa T. Calvadores s
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5
Mathematics
Fourth Quarter
Module 1: Finding the Area of
a Given Circle
INTRODUCTION
This module is written in support of the K to 12 Basic Education Program to
ensure attainment of standards expected of you as a learner. This aims to equip you
with essential knowledge on finding area of a circle.
This includes the following activities/tasks:
• Expected Learning Outcome-This lays out the learning outcome that you are
expected to have accomplished at the end of the module.
• Pre-test- This determines your prior learning on the particular lesson you are
about to take.
• Discussion of the Lesson-This provides you with the important knowledge,
principles and attitude that will help you meet the expected learning outcome.
• Learning Activities- These provide you with the application of the knowledge
and principles you have gained from the lesson and enable you to further
enhance your skills as you carry out prescribed tasks.
• Post test- This evaluates your overall understanding about the module. With
the different activities provided in this module, may you find the material
engaging and challenging as it develops your critical thinking skills.
What I Need to Know
At the end of this lesson, you will be able to:
find the area of a given circle. (M5ME-Iva-74)
What I Know
Find the area of a circle. Write the answer in your notebook. (Note that
the circles are not drawn to scale.)
13 ft
1) 3)
6 dm
2) 4)
12 in 8m
What’s In
Find the circumference of each circle. Use 3.14 for the value of π. (Note
that the circles are not drawn to scale.)
4 cm
1) 2)
9 dm
What’s New
A street sweeper is working on her area when she noticed an open manhole.
For the safety of the pedestrians, she knows that she must find a cover for the
manhole. She found an old manhole cover in their stock room that that has a top
surface area of 3 000 square meters (cm 2). If the diameter of the open manhole is
60 cm, would the old manhole cover be useful?
What Is It
If we want to know the space covered by the interior of the circle, we refer to it
as the area. The area of a circle with radius r is given by the formula: A = r x r x π or
A = πr2.
To know if the street sweeper would be able to use the cover that she found in
their stock room, we have to compare the area of the manhole to the area of the
cover.
Given that the diameter of the manhole is 60 cm, we know that the radius is
30 cm.
Use the formula: A = πr2.
A = πr2.
A = 3.14 x 302
A = 3.14 x 30 x 30
A = 3.14 x 900
A = 2 826 square centimeters (cm2)
The area of the open manhole is 2 826 cm2.
The area of the old manhole cover as given in the problem is 3 000 cm2 which
is obviously too big for the hole.
Well, could the street sweeper have used it? Perhaps for a while, until she
finds a cover that will exactly fit the open manhole.
In the circle above, the space with grid lines is the area. Its diameter is 6
units and radius is 3 units. If you count the number of square units, it will have about
28 square units.
Using the formula A = πr2
A = πr2
A = 3.14 x 32
A = 3.14 x 3 x 3
A = 3.14 x 9
A = 28.26 square units
In finding the area of a circle, the unit of measure to be used should be in square
units.
Given Unit Unit of Measure to be Used for the Area
Millimeters (mm) Square millimeters, sq mm or mm2
Centimeters (cm) Square centimeters, sq cm or cm2
Decimeters (dm) Square decimeters, sq dm or dm2
Meters (m) Square meters, sq m or m2
Inches (in) Square inches, sq in or in2
Feet (ft) Square feet, sq ft or ft2
Yards (yd) Square yards, sq yd or yd2
Let us have more examples in finding the area of a circle below.
Example 1. Find the area of the circle with a radius of 12 centimeters.
A = πr2
A = 3.14 x 122
A = 3.14 x 12 x 12
A = 3.14 x 144
A = 452.16 square centimeters or 452.16 cm2
Example 2. Find the area of the circle with a diameter of 16 meters.
(Since the given dimension is a diameter, divide 16 by 2 to get the radius. So, the
radius is 8.)
A = πr2
A = 3.14 x 82
A = 3.14 x 8 x 8
A = 3.14 x 64
A = 200.96 square decimeters or 200.96 dm2
What’s More
1. A circular flower garden has a diameter of 10 meters. Find the area of the
flower garden?
2. Carla has a circular tablecloth. Its radius is 1.5 cm. What is its area?
What I Have Learned
I have learned that:
The area of a circle is the number of square units inside that
circle. It can be computed by A = πr2.
What I Can Do
Find the area of the circle with the given diameter or radius. Write your
solutions and answers in your notebook.
1. d = 18 cm
2. r = 2.5 feet
Assessment
Find the area of the following. Write the answer in your notebook.
(π = 3.14)
1) 2)
14dm
6 cm
3) r = 1.2 m 4) d = 8 cm
Answer Key
What I know
1) 530.66 square feet
2) 452.16 square inches
3) 28.26 square decimeters
4) 50.24 square meters
What’s In
1) 25.12 cm
2) 28.26 dm
What’s More
1) 78.5 square meters
2) 7.065 square centimeters
What I Can Do
1) 254.34 square centimeters
2) 19.625 square feet
Assessment (2 points – 1 for the number and 1 for the label)
1) 28.26 square centimeters
2) 153.86 square decimeters
3) 4.5216 square meters
4) 50.24 square centimeters
References
DepEd LEARNING RESOURCE MANAGEMENT and DEVELOPMENT
SYSTEM PORTAL
INSTRUCTIONAL MATERIALS COUNCIL SECRETARIAT, 2011
21st Century MATHletes, Lumbre, et.al, 2016
LR Portal
https://www.mathgoodies.com/lessons/vol2/circle_area
https://www.piday.org/calculators/circumference-calculator/
