4 A's SEMI-DETAILED LESSON PLAN IN MATHEMATICS 7

I. Objectives
At the end of 60-minute class discussions and class activities, the learners of
Grade 7 of Baliguian National High School are expected to learn the following, with
at least 75% level of accuracy and proficiency:
a. define Polya’s problem solving techniques;
b. solves problems involving sides and angles of a polygon
(M7GE-IIIj-1); and
c. realize the importance of polygons in real-life.

II. Subject Matter

Topic: Problem Solving Involving Sides and Angles of a Polygon
Materials: Visual aids and chalkboard
Reference: Department of Education Mathematics - 7 Learner's Module
https://depedtambayan.net

III. Instructional Procedure

A. Daily Routine/Preliminary Activities
1. Prayer
2. Greetings
3. Setting Arrangement
4. Checking of Attendance
5. Setting of Standard
6. Review of the past lessons
B. Activity (Show Me Board)

Trivia Question: In what city can we find the largest church in the world?

Match column A with column B, then write the letter of the correct answer to each number.

COLUMN A COLUMN B

A. PENTAGON 1. 10 sides
C. NONAGON 2. 5 sides
I. QUADRILATERAL 3. 7 sides
L. TRIANGLE 4. 4 sides
N. HEXAGON 5. 9 sides
T. HEPTAGON 6. 5 angles
V. DECAGON 7. 6 sides
Y. OCTAGON

V A T I C A N_
1 2 3 4 5 6 7

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C. Analysis

The students will answer the following questions:

 In what city can we find the largest church in the world?

 Is there any relationship with regards to our topic?

D. Abstraction

SOLVING PROBLEMS INVOLVING

SIDES AND ANGLES OF A POLYGON

REMEMBER:
 The word polygon is a Greek word. Poly means many and gon
means angle.
 A polygon is a flat or plane figure, two dimensional closed
shape with straight sides. It does not have curved sides.
 The angles formed by the sides of a polygon are called interior
angles of a polygon. The angles formed where its sides are
extended are called exterior angles of a polygon.
 The sum of the interior angles of a convex polygon with n
sides is given by S = (n – 2) 180º.
 The sum of the exterior angles of a convex polygon (one at
each vertex) is 360º.
 The measure of each interior angle of a regular polygon
( n−2 ) 180 º
represented as r is r = .
n
 Regular polygon is an equiangular (equal angles) and
equilateral (equal sides) polygon.
 The interior angle and its adjacent exterior angle form a linear
pair. It means that the sum of their measures is 180º.

We should follow a systematic procedure in solving problems such as the

Polya’s problem solving techniques which highlight the following steps in solving
the given problem.

STEP 1: Understand the problem.

STEP 2: Devise a plan.

STEP 3: Carry out the plan.

STEP 4: Look back.

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PROBLEM 1:

Liza received a regular hexagonal jewelry storage from her mom as a Christmas gift.
It its perimeter is 120 cm, what is the measure of each side of the said storage?

Polya’s Problem Solving Techniques

 In the given problem, our goal is to solve for the measure of each side of
the hexagonal storage given the perimeter of 120 cm.

 The perimeter of a hexagonal is the sum of the measures of its six sides.
And since the perimeter is given, we need to divide it to six to find the
measure of each side.

 Let’s solve this problem.

Solution:

Let P = perimeter of the regular hexagon and s = the measure of each side

P = 6s
120 cm = 6s
120 cm 6 s
=
6 6
20 cm = s
s = 20 cm

 Since we already know the answer, we can now interpret. Therefore, each
side of the regular hexagonal jewelry storage measures 20 cm.

PROBLEM 2:

Given the figure below, determine the unknown measure of the exterior angle.

 Our goal is to solve for the measure of each exterior angle of the given
figure.

 Notice that in the given figure, the interior and exterior angles are
considered as linear pair. Therefore, the sum of their measures is always
180º.

 Solution

100º + m∠ x = 180º

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 100º + m∠ x + (-100º) = 180º + (-100º)

m∠ x = 80º

 Therefore, the m∠ x = 80º.

PROBLEM 3:

Rosa was assigned to measure all the interior angles of heptagon. What is the sum of
the measures of all its interior angles?

 Our goal is to solve for the sum of the measures of all its interior angles of
a heptagon.

 Consider the formula in finding the sum of the interior angle of a polygon
and that a heptagon is a 7-sided polygon.

 Solve

S = (n – 2) 180º
S = (7 – 2) 180º
S = (5) 180º
S = 900º

 Therefore, the sum of the measures of all the interior angles of heptagon is
900º.

PROBLEM 4:

In their Mathematics group activity, Ryan was assigned to measure the exterior angles
of a regular octagon. What is the measure of each exterior angle of a regular octagon?

Solution:
Let x = be the measure of each exterior angle
n = number of sides of a polygon = 8

Formula: S = (n – 2) 180º
= (8 – 2) 180º
= (6) 180º
= 1, 080º

1, 080 º
Interior Angle =
x 8
= 135º
Exterior Angle = 180º - 135º
So, x = 45º

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 E. Application
Problem Solved!
Directions: Solve the following problems. Write your solutions on a separate sheet of
paper.

1. Rommel created variety of quadrilateral designs for his project. What is the sum of
all the interior angles of each quadrilateral?
Answer: S = (n – 2) 180º
= (4 – 2) 180º
= (2) 180º
S = 360º
2. Teacher Sherry assigned Rhea to draw a polygon whose sum of the measure of the
interior angles is 1,260º. What kind of polygon does she need to draw?
Answer: S = (n – 2) 180º
1,260 = (n – 2) 180º
1,260 = 180 n - 360
1,260 + 360 = 180 n
1,620 180 n
=
180 180
9=n
3. Your teacher gave you a 200 cm wire. She asked you to make a regular polygon out
of it. Answer the following questions by completing the table.
a. What is the measure of each side?
b. what is the sum of its interior angles?
c. What is the measure of each interior angle?
d. What is the measure of each exterior angle?

Polygon Measure of Sum of the Measure of Measure of

each side Interior angles each Interior each exterior
angle angle
Square 50 cm 360º 90º 90º
Pentagon 40 cm 540º 108º 72º
Octagon 25 cm 1,080º 135º 45º

F. Generalization

 A polygon is a flat or plane figure, two dimensional closed shape with

straight sides. It does not have curved sides.
 The angles formed by the sides of a polygon are called interior angles of a
polygon. The angles formed where its sides are extended are called
exterior angles of a polygon.
 In finding the Sum of the interior angles, use the formula S = (n – 2) 180º.

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  In getting of each interior angle of a regular polygon is to divide the sum
of the interior angles to the number of sides.
 Also, in finding the exterior angle of a regular polygon is to subtract 180º
and the said interior angle.

IV. Evaluation

Directions: Read and understand each item them write the letter of the correct answer
on your answer sheet ¿).

1. It is a flat or plane figure, two dimensional closed shape with straight sides. It does not
have curved sides.
A. Polygon B. Circle C. Square D. Star

2. Which is the measure of the largest exterior angle?

A. 70º B. 80º C. 90º D. 100º
3. Do you agree that the angles formed by the sides of a polygon are called interior angles
while the angles formed where its sides are extended are called exterior angles of a polygon?
A. Yes B. No C. Maybe D. No answer

4. The surface of a stop sign is in the shape of a regular octagon. What is the sum of its
interior angles?
A. 360º B. 540º C. 1,080º D. 1,440º

5. Refer to item no. 4, what is the measure of each interior angle of the sign?
A. 110º B. 120º C. 130º D. 135º

V. Assignment

Read other example about solving problems involving sides and angles of a
polygon.

Prepared by:

JANVIE A. CADAVEDO
Student Teacher