Lesson Notes
The Perimeter of a Regular Polygon
This section will focus on how to calculate
the Perimeter of a Regular Polygon.
Regular Pentagon
We recall that a polygon is regular if all of
its sides are congruent and if all its interior
angles are congruent.
Remember that congruent means identical.
The regular polygons that we will focus on in
this section are:
# of sides(n) = 5
Regular Hexagon
Equilateral Triangle
# of sides(n) = 3
Square
# of sides(n) = 6
Regular Octagon
# of sides(n) = 4
# of sides(n) = 8
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Lesson Notes
P = ( n )( b )
Regular Decagon
Finally, we calculate the perimeter (P).
P = ( n )( b )
P = (10 )( 3cm )
P = 30cm
So, the perimeter of the regular decagon is
30cm.
# of sides(n) = 10
Let’s try a different type of question where
we are given the perimeter of a regular
polygon and we want to calculate the length
of one of its sides.
In order to calculate the perimeter of any
of the regular polygons, we will use the
formula:
P = ( n )( b )
The perimeter of the regular pentagon given
below is 35cm. Determine the value of x.
“P” is the Perimeter
“n” is the number of sides
“b” is the side length
Let’s try an example using this formula.
Calculate the perimeter of the regular
decagon given below.
First, we state the information that we know
about the regular pentagon.
P = 35cm
n = 5
b=x
Next, we state the formula to calculate the
perimeter (P) of a regular pentagon.
P = ( n )( b )
First, we state the information that we know
about the regular decagon.
b = 3cm
n = 10
Next, we state the formula to calculate the
perimeter (P) of a regular decagon.
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Lesson Notes
Finally, we calculate the value of x.
Example
P = ( n )( b )
1.
35cm = ( 5 )( x )
Calculate the perimeter of the
equilateral triangle below.
35cm ( 5 )( x )
=
5
5
( 5 )( x )
7cm =
5
x = 7cm
Step 1: Statebthe
information you know
= 7cm
about the triangle.
So, all of the sides of the regular pentagon
measure 7cm in length.
n=3
b = 7cm
P = ( n )( b )
We are ready to do more challenging
examples.
n=3
( )( )
P the
= formula
n b to calculate
Step 2: State
b = 7cm
the perimeter (P) of an equilateral
triangle.
n=3
P = ( n )( b )
Step 3: Calculate the perimeter (P).
P = ( n )( b )
P = ( 3)( 7cm )
P = 21cm
So, the perimeter of the equilateral
triangle is 21cm.
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Lesson Notes
2.
3.
The perimeter of the square given below
is 24cm. Determine the value of x.
Calculate the perimeter of the regular
pentagon given below.
=5
Step 1: Statenthe
information you know
about the pentagon.
P = 24cm
Step 1: State the information you know
n=4
about the square.
b = 3cm
Pn==(5n )( b )
b P= =x 24cm
P =n (=n4)( b )
b = 3cm
n=5
( )( )
b=x
P = 24cm
Pn == 4n )( b ) to calculate
Step 2: State the(formula
= xof a square.
the perimeterb(P)
P the
= formula
n b to calculate
Step 2: State
= 3cm
the perimeterb(P)
of a regular pentagon.
P = ( n )( b )
P = ( n )( b )
Step 3: Calculate the perimeter (P).
P = ( n )( b )
Step 3: Calculate the value of x.
P = ( n )( b )
P = ( 5 )( 3cm )
24cm = ( 4 )( x )
P = 15cm
24cm ( 4 )( x )
=
4
4
( 4 )( x )
6cm =
4
So, the perimeter of the regular
pentagon is 15cm.
x = 6cm
The value of x is 6cm.
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Lesson Notes
4.
5.
The perimeter of the regular hexagon
given below is 72cm. Determine the
value of x.
A regular octagon has a side length of
11cm. Calculate the octagon’s perimeter.
Step 1: State the information you know
about the octagon.
b = 11cm
n=8
Step 2: State the formula to calculate
the perimeter of a regular octagon.
P = ( n )( b )
Step 3: Calculate the perimeter (P).
P = ( n )( b )
P = 72cm
Step 1: State the information you know
n=6
about the hexagon.
b=x
P = 72cm
P =n(=n )(
6 b)
b=x
P = 72cm
Pn==(6n )( b )
Step 2: State the formula to calculate
the perimeterbof=axregular hexagon.
P = ( 8 )(11cm )
P = 88cm
So, the perimeter of the regular octagon
is 88cm.
P = ( n )( b )
Step 3: Calculate the value of x.
P = ( n )( b )
72cm = ( 6 )( x )
72cm ( 6 )( x )
=
6
6
( 6 )( x )
12cm =
6
x = 12cm
The value of x is 12cm.
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5