Q3 Math7 Las11
Q3 Math7 Las11
Q3 Math7 Las11
Grade 7 Mathematics
LEARNING ACTIVITY SHEET 11
PROBLEMS INVOLVING SIDES AND ANGLES OF A POLYGON
In our day to day living, geometric construction plays a vital role. Part of it is a regular
polygon. These has many applications in our daily life. In this activity sheet, you will learn to solve
real life problems involving sides and angles of a polygon.
At the end of this learning activity sheet, you should be able to solve problems involving
sides and angles of a polygon. M7GE-IIIJ-1
The following formula must be remembered in calculating unknown parts of regular polygon.
360°
Number of sides (n) =
measure of each exterior angle
Sum of interior angles = (n – 2)180
Sum of exterior Angles = 360
(n – 2)180
Measure of each interior angle =
n
360
Measure each exterior angle =
number of sides ( n )
In solving problems, we should follow a systematic procedure. Here are some examples for you.
Example 1: 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?
Step 1: Understand the Problem. In the given problem, our goal is to solve for the measure of each
exterior angle of a regular octagon.
Step 2: Make Plan 1. The sum of the measure of the exterior angles of any polygon is 360° and a
regular polygon has equal measures of angles and sides. It means that we just need to divide 360°
to number of sides of the regular polygon to determine the measure of each exterior angle.
Step 4 : Look back. Therefore, the measure of each exterior angle of a regular octagon is 45°.
Example 2: Find the sum of the measures of the interior angles of a convex hexagon.
Step 1: Understand the Problem . Understand the Problem. The problem asked to determine the sum
of the measures of the interior angles of a convex hexagon.
Step 2: Make Plan Since the number of sides of a hexagon is six, we will use the formula ,
Sum of interior angles = (n – 2)180.
Step 3: Carry Out Plan.
Given: n = 6
Solution:
Sum of interior angles = (n – 2)180 Formula for finding sum of interior angles
Sum of interior angles = (6 – 2)180 Substitution
Sum of interior angles = (4)180 Simplify expressions inside the parenthesis
Sum of interior angles = 720 Multiply
Step 4: Look back. Therefore, the sum of the measure of the interior angles of a convex hexagon is
720.
Example 3: The measure of each exterior angle of a regular polygon is 120. Find the number of
sides of the given polygon.
Step 1: Understand the Problem. The problem asked to determine the number of sides of the given
polygon given that the measure of each exterior angle is 120.
Step 2: Make Plan. Since the measure of each exterior angle of the regular polygon is 120, and the
sum of the measure of the exterior angles of a polygon is always 360, we will simply divide 360 by
120 to determine the number of sides of it.
Step 4: Look back. Therefore, the number of sides of the polygon is 3, and it is a triangle.
Example 4: The floor of a building comes in a shape of regular pentagon. Determine the measure
of each interior angle.
Step 1: Understand the Problem. The problem asked to determine the measure of each interior
angle of a regular pentagon.
Step 4: Look back. Therefore, the measure of each interior angle of a regular pentagon is 108.
3. If the perimeter of the hexagon is 360 4. If the perimeter of the octagon is 1200
cm, what is the measure of side AB? cm, what is the measure of side RS?
ACTIVITY 3
POINTS 3 2 1
Accuracy No error committed There is 1 Two or more errors
on the step by step committed error on committed on the
process the step by step step by step
process process
Neatness Very clean An erasure or More erasure on the
presentation of tampering occur on process
solution / output the step by step
process
Activity 1 Activity 2
Nivera, Gladys C., Grade 7 Mathematics Patterns and Practicalities. Salesian by Don Bosco Press,
Makati City, 2014
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